analysis of a coupled system of kinetic equations and conservation laws rigorous derivation and existence theory via defect measures in this paper we introduce a coupled system of kinetic equations of b g k type and then study its hydrodynamic limit we obtain as a consequence the rigorous derivation and existence theory for a coupled system of kinetic equations and their hydrodynamic conservation laws limit the latter is a particular case of the coupled system of boltzmann and euler equations a fundamental element in this study is the rigorous derivation and justification of the interface conditions between the kinetic model and its hydrodynamic conservation laws limit which is obtained using a new regularity theory introduced herein

a smooth transition model between kinetic and diffusion equations this paper presents a model which provides a smooth transition between a kinetic and a diffusion domain the idea is to use a buffer zone in which both diffusion and kinetic equations will be solved the solution of the original kinetic equation will be recovered as the sum of the solutions of these two equations we use an artificial connecting function which makes the equation on each domain degenerate at the end of the buffer zone thus no boundary condition is needed at the transition point this model avoids the delicate issue of finding the interface condition or iteration in a typical domain decomposition method that couples a kinetic equation with hydrodynamic equations a new asymptotic preserving method for this model is introduced and numerical examples are used to validate this new model and the new numerical method

fluid dynamic limits of kinetic equations i formal derivations the connection between kinetic theory and the macroscopic equations of fluid dynamics is described in particular our results concerning the incompressible navier stokes equations are based on a formal derivation in which limiting moments are carefully balanced rather than on a classical expansion such as those of hilbert or chapman enskog the moment formalism shows that the limit leading to the incompressible navier stokes equations like that leading to the compressible euler equations is a natural one in kinetic theory and is contrasted with the systematics leading to the compressible navier stokes equations some indications of the validity of these limits are given more specifically the connection between the diperna lions renormalized solution of the classical boltzmann equation and the leray solution of the navier stokes equations is discussed

the radiative transfer equations diffusion approximation under accretiveness and compactness assumptions abstract when the mean free path of photons is small the radiative transfer equations may be approximated by a nonlinear angular diffusion equation in order to find the diffusion equation one uses accretiveness assumptions but theses assumptions impose some conditions on the opacity to overcome this inconvenient we propose to study the solution of the radiative transfer equations by compactness techniques

l 1 convergence to the barenblatt solution for compressible euler equations with damping we study the asymptotic behavior of compressible isentropic flow through a porous medium when the initial mass is finite the model system is the compressible euler equation with frictional damping as t the density is conjectured to obey the well known porous medium equation and the momentum is expected to be formulated by darcy s law in this paper we prove that any l weak entropy solution to the cauchy problem of damped euler equations with finite initial mass converges strongly in the natural l1 topology with decay rates to the barenblatt profile of the porous medium equation the density function tends to the barenblatt solution of the porous medium equation while the momentum is described by darcy s law the results are achieved through a comprehensive entropy analysis capturing the dissipative character of the problem

a domain decomposition method for semilinear hyperbolic systems with two scale relaxations we present a domain decomposition method on a semilinear hyperbolic system with multiple relaxation times in the region where the relaxation time is small an asymptotic equilibrium equation can be used for computational efficiency an interface condition is provided to couple the two systems in a domain decomposition setting a rigorous analysis based on the laplace transform on the l2 error estimate is presented for the linear case which shows how the error of the domain decomposition method depends on the smaller relaxation time and the boundary and interface layer effects the given convergence rate is optimal we present a numerical implementation of this domain decomposition method and present some numerical results in order to study the performance of this method

on the initial boundary value problem for the bipolar hydrodynamic model for semiconductors abstract the global existence and zero relaxation limit results of weak solutions of the initial boundary value problem to the bipolar hydrodynamic model for semiconductors are established by the theory of compensated compactness the boundary conditions of weak solutions in the sense of traces are discussed

almost global existence of classical discontinuous solutions to genuinely nonlinear hyperbolic systems of conservation laws with small bv initial data abstract in the present paper the author investigates the initial problem for genuinely nonlinear quasilinear hyperbolic systems of conservation laws under small bv perturbations of the riemann initial data where the perturbations are in bv but they are assumed to be c 1 smooth with bounded and possibly large c 1 norms combining the techniques employed by li and kong with the modified glimm s functional the author obtains the almost global existence and lifespan of classical discontinuous solutions to the above problem this result is also applied to the system of one dimensional isentropic flow

the generalized nonlinear initial boundary riemann problem for linearly degenerate quasilinear hyperbolic systems of conservation laws abstract this work is a continuation of our previous work in the present paper we study the generalized nonlinear initial boundary riemann problem with small bv data for linearly degenerate quasilinear hyperbolic systems of conservation laws with nonlinear boundary conditions in a half space t x t 0 x 0 we prove the global existence and uniqueness of piecewise c 1 solution containing only contact discontinuities to a class of the generalized nonlinear initial boundary riemann problem which can be regarded as a small bv perturbation of the corresponding nonlinear initial boundary riemann problem for general n n linearly degenerate quasilinear hyperbolic system of conservation laws moreover this solution has a global structure similar to the one of the self similar solution u u x t to the corresponding nonlinear initial boundary riemann problem some applications to quasilinear hyperbolic systems of conservation laws arising in the string theory and high energy physics are also given

control of modeling errors in the coupling of linear transport and diffusion models we consider in this paper the initial boundary value problem for the 1d neutron transport equation with isotropic scattering set in some bounded interval with inflow boundary conditions the usual parabolic scaling yields the diffusive limit a surrogate model coupling transport and diffusion equations is then introduced in order to accurately assess the value of specific quantities of interest the control of the quality of the computation with respect to such a quantity of interest is performed by means of an approach for modeling error estimation combined with an adaptive strategy to control the surrogate model if necessary

symmetries and global solvability of the isothermal gas dynamics equations we study the cauchy problem associated with the system of two conservation laws arising in isothermal gas dynamics in which the pressure and the density are related by the law equation p with 1 our results complete those obtained earlier for 1 we prove the global existence and compactness of entropy solutions generated by the vanishing viscosity method the proof relies on compensated compactness arguments and symmetry group analysis interestingly we make use here of the fact that the isothermal gas dynamics system is invariant modulo a linear scaling of the density this property enables us to reduce our problem to that with a small initial density

a multivariate signed rank test for the one sample location problem abstract an affine invariant signed rank test is proposed for the one sample multivariate location problem the test suggested is a modification of randles s multivariate sign test based on interdirections which extends blumen s bivariate procedure to the multidimensional setting comparisons are made between the proposed statistic and several competitors via pitman asymptotic relative efficiencies and monte carlo results the signed rank statistic appears to be robust it performs better than its competitors when the distribution is light tailed and virtually as well as hotelling s t 2 under multivariate normality for heavy tailed distributions the signed rank statistic performs better than hotelling s t 2 but not as well as randles s statistic

averaging regularity results for pdes under transversality assumptions let u u x y and f f x y be two functions related by a pde p x y dx dy u f the regularity of the y average u x dy as a function of x is investigated knowing that of u and f our method consists in reducing p to a microlocal normal form under a natural transversality assumption the 2 microlocal regularity of u is also determined knowing that of f these results are then applied to a homogenization problem this article generalizes the results of 16 and 12 on velocity averaging and homogenization for kinetic equations

diffusion approximation and computation of the critical size this paper is devoted to the mathematical definition of the extrapolation length which appears in the diffusion approximation to obtain this result we describe the spectral properties of the transport equation and we show how the diffusion approximation is related to the computation of the critical size the paper also contains some simple numerical examples and some new results for the milne problem introduction the computation of the critical size and the diffusion approximation for the transport equation have been closely related and this is due to the following facts first the computation of the critical size is much easier for the diffusion approximation than for the original transport equation second for the critical size one can consider a host media x nxq with x0 given and 17 a positive number the problem of the critical size is then reduced to the computation of the parameter zj it turns out that when the transport operator is almost conservative the critical value of the parameter 17 is large and it is exactly for this range of value that the diffusion approximation is accurate on the other hand the physical boundary condition for the diffusion approxi mation is of the form

convergence of the viscosity method for isentropic gas dynamics a convergence theorem for the method of artificial viscosity applied to the isentropic equations of gas dynamics is established convergence of a subsequence in the strong topology is proved without uniform estimates on the derivatives using the theory of compensated compactness and an analysis of progressing entropy waves

l1 convergence rates to the barenblatt solution for the damped compressible euler equations abstract in our previous work 17 it is shown that any l weak entropy solution of damped compressible euler equation converges to the barrenblatt s solution with finite mass in l 1 norm with a convergence rate for 1 3 in this paper by introducing an elaborate iterative method and using the intensive entropy analysis we prove the l 1 convergence to the barrenblatt s solution for any large 3 furthermore we get better l 1 convergence rate for 2 3

fluid dynamic limits of kinetic equations ii convergence proofs for the boltzmann equation using relative entropy estimates about an absolute maxwellian it is shown that any properly scaled sequence of diperna lions renormalized solutions of some classical boltzmann equations has fluctuations that converge to an infinitesimal maxwellian with fluid variables that satisfy the incompressibility and boussinesq relations moreover if the initial fluctuations entropically converge to an infinitesimal maxwellian then the limiting fluid variables satisfy a version of the leray energy inequality if the sequence satisfies a local momentum conservation assumption the momentum densities globaly converge to a solution of the stokes equation a similar discrete time version of this result holds for the navier stokes limit with an additional mild weak compactness assumption the continuous time navier stokes limit is also discussed 01993 john wiley sons inc

analysis of the m1 model well posedness and diffusion asymptotics abstract this paper is devoted to the analysis of the m 1 model which arises in radiative transfer theory the derivation of the model is based on the entropy minimization principle which leads to a hyperbolic system of balance laws with relaxation in the multi dimensional case we establish the existence uniqueness of a globally defined smooth solution under a suitable smallness condition on the initial data in the one dimensional case we show that the smallness condition does not depend on the particles mean free path so that we can also rigorously justify the consistency of the model with the diffusion asymptotics the result extends the analysis of coulombel et al j f coulombel f golse t goudon diffusion approximation and entropy based moment closure for kinetic equations asymptotic analysis 45 2005 1 39 to the case where the entropy functional accounts for relaxation towards the planckian state which is physically more relevant

using concept lattice theory to obtain the set of solutions of multi adjoint relation equations an important goal in the fuzzy relation equations framework is to obtain the whole set of solutions this paper introduces algebraic properties in the multi adjoint concept lattice setting moreover using the relationship between these concept lattices and multi adjoint relation equations the complete set of solutions of these general equations is characterized and computed avoiding the necessity of considering minimal solutions

domain decomposition for compressible navier stokes equations with different discretizations and formulations the purpose of this work is to couple different numerical models and approximations for the calculation of high speed external flows governed by the compressible navier stokes equations the proposed coupling is achieved by the boundary conditions which impose viscous fluxes and friction forces on the body for the calculation of the global external flow and which impose dirichlet type boundary conditions on the interface for the local model

a kinetic equation with kinetic entropy functions for scalar conservation laws we construct a nonlinear kinetic equation and prove that it is welladapted to describe general multidimensional scalar conservation laws in particular we prove that it is well posed uniformly in e the microscopic scale we also show that the proposed kinetic equation is equipped with a family of kinetic entropy functions analogous to boltzmann s microscopich function such that they recover krushkov type entropy inequality on the macroscopic scale finally we prove by both bv compactness arguments in the multidimensional case and by compensated compactness arguments in the one dimensional case that the local density of kinetic particles admits a continuum limit as it converges strongly with e 0 to the unique entropy solution of the corresponding conservation law

the milne problem for the radiative transfer equations with frequency dependence we study the following stationary frequency dependent transport equation 28xf a t f bv t o x o m o u e 1 1 tr t bv t fjdm 8 0 r x 1 1 2 f 2 w 2 0 u e j0 1 where bv is the well known planck function appearing in astrophysics we are able to describe the asymptotic behavior of f and t for x large when a t is of the special form a t tr m k t our method relies mainly on the monotonicity of the nonlinearity the proof does not use any linearization of the equation in particular no smallness assumption on the data yp in any sense is required resume nous etudions l equation de transport stationnaire avec dependance en frequence 2dxf a t f bv t o x o m o u e 1 1 tr t bv t fjdm 8 0 r x 1 1 2 8 2 w 2 o u e 0 1 lorsque a t est de la forme particuliere a t a m k t nous savons decrire le comportement asymptotique de f et t pour x grand notre methode repose principalement sur la monotonie de la non linearite la preuve n utilise aucune linearisation de l equation en particulier nous n avons besoin d aucune hypothese de petitesse d aucune sorte sur la donnee y

multi adjoint relation equations definition properties and solutions using concept lattices this paper generalizes fuzzy relation equations following the multi adjoint philosophy moreover the solutions of these general fuzzy relation equations and the concepts of a multi adjoint property oriented concept lattice are related and several results are obtained from the theory of concept lattices as a consequence of this relevant relation more properties about these general equations can be proven from the theory of concept lattices and the algorithms developed to compute concept lattices can be used to obtain solutions furthermore an interesting application to fuzzy logic programming has been introduced in which an important problem in this topic has been interpreted in terms of solving a multi adjoint relation equation

coupling boltzmann and navier stokes equations by friction the aim of this paper is to introduce and validate a coupled navier stokes boltzman approach for the calculation of hypersonic rarefied flows around manoeuvering vehicles the proposed strategy uses locally a kinetic model in the boundary layer coupled through wall friction forces to a global navier stokes solver dif ferent numerical experiments illustrate the potentialities of the method

upwinding of the source term at interfaces for euler equations with high friction we consider euler equations with a friction term that describe an isentropic gas flow in a porous domain more precisely we consider the transition between low and high friction regions in the high friction region the system is reduced to a parabolic equation the porous media equation in this paper we present a hyperbolic approach based on a finite volume technique to compute numerical solutions for the system in both regimes the upwind source at interfaces usi scheme that we propose satisfies the following properties firstly it preserves the nonnegativity of gas density secondly and this is the motivation the scheme is asymptotically consistent with the limit model porous media equation when the friction coefficient goes to infinity we show analytically and through numerical results that the above properties are satisfied we shall also compare results given with the use of usi hyperbolic parabolic coupling and classical centered sources schemes

existence theory for the isentropic euler equations we establish an existence theorem for entropy solutions to the euler equations modeling isentropic compressible fluids we develop a new approach for constructing mathematical entropies for the euler equations which are singular near the vacuum in particular we identify the optimal assumption required on the singular behavior on the pressure law at the vacuum in order to validate the two term asymptotic expansion of the entropy kernel we proposed earlier for more general pressure laws we introduce a new multiple term expansion based on the bessel functions with suitable exponents and we also identify the optimal assumption needed to validate the multiple term expansion and to establish the existence theory our results cover as a special example the density pressure law where and are arbitrary constants

existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in eulerian and lagrangian coordinates we prove the existence and compactness stability of entropy solutions for the hyperbolic systems of conservation laws corresponding to the isentropic gas dynamics where the pressure and density are related by a law for any 1 our results considerably extend and simplify the program initiated by diperna and provide a complete existence proof our methods are based on the compensated compactness and the kinetic formulation of systems of conservation laws 1996 john wiley sons inc

global solutions and stability for self gravitating isentropic gases abstract the global solution to the radial motion of self gravitating gases is studied the global approximate solutions are constructed by a generalized shock capturing method the nonlocal terms are carefully estimated the uniform estimate of the approximate solutions is obtained the convergence of the approximate solutions is proved by the compensated compactness method the global existence of weak entropy solution with arbitrarily large l initial data is then established

rigorous derivation and analysis of coupling of kinetic equations and their hydrodynamic limits for a simplified boltzmann model in this paper we derive rigorously the coupling of kinetic equations and their hydrodynamic limits for a simplified kinetic model we prove the global convergence of the chapman enskog expansion for this model we then study the existence theory and asymptotic behaviour of the coupled systems to solve the coupled problems we propose to use the transmission time marching algorithm we then develop a convergence theory for the resulting algorithms

system of fuzzy relation equations with inf composition complete set of solutions the problem of solvability of a system of equations with inf composition is considered on finite universes equations are expressed using operations of a bl algebra we study complete set of solutions of the respective system in the particular case one equation and in the general case in both cases various conditions of solvability are found and proved we characterize all maximal solutions and prove that under certain conditions each solution of the system an equation is less than or equal to a respective maximal one as a result we are able to characterize the complete set of solutions examples of single equations and their systems are considered and complete sets of solutions are found for each

the nonaccretive radiative transfer equations existence of solutions and rosseland approximation we present an existence theory and an asymptotic analysis for the radiative transfer equations ue t xuee ue e2 ue ue 0 inx 1 ue x sn k ue t 0 u0 where u u t x t r x x rn 1 sn and ue t x 1 sn ue t x d we prove that even if has a singularity 0 1 has a solution ue l r x sn as e 0 we show that ue converges pointwise to a function u l r x solution of the degenerate parabolic equation u t f u 0 in x u x k u t 0 u0 this is achieved without any monotonicity assumption on and therefore one cannot use the theory of nonlinear contraction semigroups

a rigorous derivation of the coupling of a kinetic equation and burgers equation in this article we investigate the kinetic fluid coupling on a toy model which we obtain rigorously from a hydrodynamical limit the idea is that at the level of the full kinetic model the coupling is obvious we then investigate the coupling obtained when passing into the limit we show that especially in presence of a shock stuck on the interface the coupling involves a kinetic layer known as the milne problem due to this layer the limit process is quite delicate and some blow up techniques are needed to ensure its strong convergence

the comparison of the riemann solutions in gas dynamics in this paper we compare two riemann solution constructions of isentropic and nonisentropic gas dynamic equations with the same initial values we obtain that when rarefaction waves occur in the non isentropic solution the same family rarefaction waves occur in the isentropic solution however when advancing or reflected shock waves occur in the isentropic case the same kind shock waves occur in the nonisentropic case moreover by numerical calculation it can be found that the wave intensities of the two solutions are quite close our conclusion reflects that almost non isentropic gas dynamic process can be simulated by isentropic gas dynamic process in practice c 2015 elsevier inc all rights reserved

uniqueness and stability of riemann solutions with large oscillation in gas dynamics we prove the uniqueness of riemann solutions in the class of entropy solutions in with arbitrarily large oscillation for the 3 3 system of euler equations in gas dynamics the proof for solutions with large oscillation is based on a detailed analysis of the global behavior of shock curves in the phase space and the singularity of centered rarefaction waves near the center in the physical plane the uniqueness of riemann solutions yields their inviscid large time stability under arbitrarily large perturbation of the riemann initial data as long as the corresponding solutions are in l and have local bounded total variation satisfying a natural condition on its growth with time no specific reference to any particular method for constructing the entropy solutions is needed the uniqueness result for riemann solutions can easily be extended to entropy solutions u x t piecewise lipschitz in x for any t 0 with arbitrarily large oscillation

hyperbolic to parabolic relaxation theory for quasilinear first order systems abstract in this paper we study the limiting behavior of nonhomogeneous hyperbolic systems of balance laws when the relaxed equilibria are described by means of systems of parabolic type in particular we obtain a complete theory for the 2 2 systems of genuinely nonlinear hyperbolic balance laws in 1 d with a strong dissipative term a different method which combines the div curl lemma with accretive operators is then applied to study the limiting profiles in the case of nonhomogeneous isentropic gas dynamics we also investigate relaxation results for some 2 d cases which include the cattaneo model for nonlinear heat conduction and the compressible euler flow moreover convergence result is also obtained for general semilinear systems in 1 d

new models for the solution of intermediate regimes in transport theory and radiative transfer existence theory positivity asymptotic analysis and approximations in this paper we propose derive and establish the mathematical foundations of new models for the solution of intermediate regimes in transport theory and radiative transfer these new models consist of coupling the transport equations with their diffusion approximations our mathematical theory includes the existence theory the positivity of the solutions and the asymptotic analysis we also give the rate of the asymptotic decay in order to solve the new coupled problem we propose to use the transmission time marching algorithm introduced and studied in refs 10 13 15 we then study the convergence of the resulting algorithm these studies are based in an essential way on the methods we introduced in refs 14 15

maps of convex sets and invariant regions for finite difference systems of conservation laws general results about maps of convex sets in r n are proved we outline their extensions to an infinite dimensional context such extensions have applications in nonlinear analysis such as in the study of the invariance of convex sets under nonlinear maps here we explore applications only in the finite dimensional context more specifically we apply the general results to the problem of finding sufficient conditions for a region of the state space to be globally or locally invariant under finite difference schemes applied to systems of conservation laws in several space variables in particular we establish a final characterization of the invariant regions under the lax friedrichs scheme and also give sufficient conditions for the local invariance further we give sufficient conditions for the global and local invariance of regions under flux splitting finite difference schemes an example of the multi dimensional euler equations for non isentropic gas dynamics is discussed

the use of linguistic variables and fuzzy propositions in the l fuzzy concept theory the use of linguistic variables and fuzzy propositions in the interval valued l fuzzy contexts can be an interesting tool to extract a more complete information from them in this paper we analyze three different situations first we obtain significant relations in order to study all the objects and attributes of the interval valued l fuzzy context by means of the interval valued l fuzzy concepts after that we show how to replace the erroneous values to be able to study in a suitable way the context finally we use the linguistic labels to obtain a subcontext that represents our interest of study we also show an experimental evaluation in the paper

non linear diffusions as limit of kinetic equations with relaxation collision kernels kinetic transport equations with a given confining potential and non linear relaxation type collision operators are considered general monotone energy dependent equilibrium distributions are allowed with a chemical potential ensuring mass conservation existence and uniqueness of solutions is proved for initial data bounded by equilibrium distributions the diffusive macroscopic limit is carried out using compensated compactness theory the results are drift diffusion equations with non linear diffusion the most notable examples are of the form partial t rho nabla cdot nabla rho m rho nabla v ranging from porous medium equations to fast diffusion with the exponent satisfying 0 m 5 3 in mathbb r 3

multivariate sign based high dimensional tests for the two sample location problem abstractthis article concerns tests for the two sample location problem when data dimension is larger than the sample size existing multivariate sign based procedures are not robust against high dimensionality producing tests with type i error rates far away from nominal levels this is mainly due to the biases from estimating location parameters we propose a novel test to overcome this issue by using the leave one out idea the proposed test statistic is scalar invariant and thus is particularly useful when different components have different scales in high dimensional data asymptotic properties of the test statistic are studied compared with other existing approaches simulation studies show that the proposed method behaves well in terms of sizes and power supplementary materials for this article are available online

application of maximum principles to the analysis of a coupling time marching algorithm abstract in this paper we study the convergence properties of a coupling time marching algorithm solving convection diffusion problems on two domains using incompatible approximations convergence properties are obtained using local and global estimates of the solutions of convection diffusion problems

expanding large global solutions of the equations of compressible fluid mechanics without any symmetry assumptions on the initial data we construct global in time unique solutions to the vacuum free boundary three dimensional isentropic compressible euler equations when the adiabatic exponent gamma lies in the interval 1 frac 5 3 our initial data lie sufficiently close to the expanding compactly supported affine motions recently constructed by sideris and they satisfy the physical vacuum boundary condition

formation of singularities in three dimensional compressible fluids presented are several results on the formation of singularities in solutions to the three dimensional euler equations for a polytropic ideal fluid under various assumptions on the initial data in particular it is shown that a localized fluid which is initially compressed and outgoing on average will develop singularities regardless of the size of the initial disturbance

anomalous diffusion limit induced on a kinetic equation using a compactness argument based on the velocity averaging lemma of golse et al it is shown that the limiting behavior of a kinetic linearized bgk gas model confined between two plates with maxwell boundary conditions when the distance between the plates goes to zero under a suitable anomalous scaling is diffusive we do not require the use of central limit theorems as in the method of borgers et al

convergence rate for compressible euler equations with damping and vacuum we study the asymptotic behavior of l weak entropy solutions to the compressible euler equations with damping and vacuum previous works on this topic are mainly concerned with the case away from the vacuum and small initial data in the present paper we prove that the entropy weak solution strongly converges to the similarity solution of the porous media equations in lp r 2 p with decay rates the initial data can contain vacuum and can be arbitrary large a new approach is introduced to control the singularity near vacuum for the desired estimates

bounded speed of propagation for solutions to radiative transfer equations the radiative transfer equation is the nonlinear transport equation partial t f frac 1 varepsilon v cdot nabla x f frac 1 varepsilon 2 sigma tilde f f tilde f 0 rte where tilde f x mathbf t ff x mathbf v t dv denotes the average off x t on the unit sphere v 1 it describes the absorption and emission of photons in a hot medium as the mean free path goes to 0 f converges to a solution of the porous medium equation t u f u withf u n u 1 since blows up atu 0 solutions to the pme propagate with finite speed specifically ifu 0 has compact support inr n so doesu t for everyt 0 and the sets t x u x t 0 t 0 form an expanding family ast increases andu t r n we show in this paper that these propagation properties hold for the solutionsf of the rte for all small moreover the growth of the support off is uniform in our proofs rely on the construction of explicit solutions of the travelling wave type and subsolutions to the rte to our knowledge this is the first example of a kinetic equation with high velocities where localized data propagate always with bounded speed for vlasov poisson equations this arises only for particular initial data

finite energy method for compressible fluids the navier stokes korteweg model this is the first of a series of papers devoted to the initial value problem for the one dimensional euler system of compressible fluids and augmented versions containing higher order terms in the present paper we are interested in dispersive shock waves and analyze the zero viscosity capillarity limit associated with the navier stokes korteweg system specifically we establish the existence of finite energy solutions as well as their convergence toward entropy solutions to the euler system our method of proof combines energy and effective energy estimates a nonlinear sobolev inequality high integrability properties for the mass density and for the velocity and compactness properties based on entropies 2015 wiley periodicals inc

hydrodynamic limits for kinetic equations and the diffusive approximation of radiative transport for acoustic waves we consider a class of kinetic equations equipped with a single conservation law which generate l 1 contractions we discuss the hydrodynamic limit to a scalar conservation law and the diffusive limit to a possibly degenerate parabolic equation the limits are obtained in the dissipative sense equivalent to the notion of entropy solutions for conservation laws which permits the use of the perturbed test function method and allows for simple proofs a general compactness framework is obtained for the diffusive scaling in l 1 the radiative transport equations satisfied by the wigner function for random acoustic waves present such a kinetic model that is endowed with conservation of energy the general theory is used to validate the diffusive approximation of the radiative transport equation

asymptotic preserving well balanced schemes for radiative transfer and the rosseland approximation we are concerned with efficient numerical simulation of the radiative transfer equations to this end we follow the well balanced approach s canvas and reformulate the relaxation term as a nonconservative product regularized by steady state curves while keeping the velocity variable continuous these steady state equations are of fredholm type the resulting upwind schemes are proved to be stable under a reasonable parabolic cfl condition of the type t o x2 among other desirable properties some numerical results demonstrate the realizability and the efficiency of this process

kinetic formulation of the isentropic gas dynamics and p systems we consider the 2 x 2 hyperbolic system of isentropic gas dynamics in both eulerian or lagrangian variables also called the p system we show that they can be reformulated as a kinetic equation using an additional kinetic variable such a formulation was first obtained by the authors in the case of multidimensio nal scalar conservation laws a new phenomenon occurs here namely that the advection velocity is now a combination of the macroscopic and kinetic velocities various applications are given we recover the invariant regions deduce new l estimates using moments lemma and prove l w stability for 7 3

on the classical solutions to the hydrodynamic model for semiconductors abstract this paper mainly deals with the multidimensional hydrodynamic model for semiconductors inspired by the previous papers y shizuta s kawashima systems of equations of hyperbolic parabolic type with applications to the discrete boltzmann equation hokkaido math j 14 1985 249 275 s kawashima w a yong dissipative structure and entropy for hyperbolic systems of balance laws arch ration mech anal 174 2004 345 364 w a yong entropy and global existence for hyperbolic balance laws arch ration mech anal 172 2004 247 266 we develop some new frequency localization estimates to establish the global existence and exponential stability of small classical solutions in a class of critical besov spaces which are different from estimates in our recent paper d y fang j xu t zhang global exponential stability of classical solutions to the hydrodynamic model for semiconductors math models methods appl sci 17 2007 1507 1530 furthermore this new method can also be applied to the multidimensional euler equations with damping the analytic tool used is the littlewood paley decomposition

decay of almost periodic solutions of conservation laws we consider the asymptotic behavior of solutions of systems of inviscid or viscous conservation laws in one or several space variables which are almost periodic in the space variables in a generalized sense introduced by stepanoff and wiener which extends the original one of h bohr we prove that if u x t is such a solution whose inclusion intervals at time t with respect to 0 satisfy l epsiv t t 0 as t and such that the scaling sequence u t x t u t x t t is pre compact as t in l loc 1 d 1 then u x t decays to its mean value which is independent of t as t the decay considered here is in l 1 loc of the variable x t which implies as we show that as t where m x denotes taking the mean value with respect to x in many cases we show that if the initial data are almost periodic in the generalized sense then so also are the solutions we also show in these cases how to reduce the condition on the growth of the inclusion intervals l t with t as t for fixed 0 to a condition on the growth of l 0 with as 0 which amounts to imposing restrictions only on the initial data we show with a simple example the existence of almost periodic non periodic functions whose inclusion intervals satisfy any prescribed growth condition as 0 the applications given here include inviscid and viscous scalar conservation laws in several space variables some inviscid systems in chromatography and isentropic gas dynamics as well as many viscous 2 2 systems such as those of nonlinear elasticity and eulerian isentropic gas dynamics with artificial viscosity among others in the case of the inviscid scalar equations and chromatography systems the class of initial data for which decay results are proved includes in particular the l generalized limit periodic functions our procedures can be easily adapted to provide similar results for semilinear and kinetic relaxations of systems of conservation laws

global existence to the bgk model of boltzmann equation abstract we present an existence and a stability proof for solutions to the bgk model of boltzmann equation f v x f f m f t 0 x r n v r n m f p 2 t n 2 exp v u 2 2t p pu p u 2 pt 1 x r n 1 v v 2 f t x v dv it relies on the strong compactness of u t and on a new estimate on the third moment of v dv we also prove the entropy relation for 1

solving systems of fuzzy relation equations by fuzzy property oriented concepts this paper relates systems of fuzzy relation equations with the theory of fuzzy property oriented concept lattices consequently the results obtained from this theory of concept lattices can be transformed in order to obtain properties about the former moreover the algorithms developed to obtain concept lattices can be applied to obtain solutions for systems of fuzzy relation equations

fuzzy rough nearest neighbour classification and prediction nearest neighbour nn approaches are inspired by the way humans make decisions comparing a test object to previously encountered samples in this paper we propose an nn algorithm that uses the lower and upper approximations from fuzzy rough set theory in order to classify test objects or predict their decision value it is shown experimentally that our method outperforms other nn approaches classical fuzzy and fuzzy rough ones and that it is competitive with leading classification and prediction methods moreover we show that the robustness of our methods against noise can be enhanced effectively by invoking the approximations of the vaguely quantified rough set vqrs model which emulates the linguistic quantifiers some and most from natural language

convergence analysis of domain decomposition algorithms with full overlapping for the advection diffusion problems the aim of this paper is to study the convergence properties of a time marching algorithm solving advection diffusion problems on two domains using incompatible discretizations the basic algorithm is first presented and theoretical or numerical results illustrate its convergence properties this study is based on spectral theory a priori estimates and a di giorgi nash maximum principle

multi adjoint property oriented and object oriented concept lattices this paper presents a generalisation of the classical property and object oriented concept lattices to a fuzzy environment based on the philosophy of the multi adjoint paradigm these concept lattices are generalisations of rough set theory used to consider two different sets the set of objects and the set of attributes to apply the corresponding modal operators as in formal concept analysis first of all the paper presents several specific properties of adjoint triples in which the duals of several supports are considered these properties are then used to introduce the multi adjoint property and object oriented concept lattices in which different adjoint triples can be used in non linear sets as well as the corresponding representation fundamental theorems moreover these lattices are related to the multi adjoint concept lattice in which negation operators are not needed as a result this relation allows the properties to be translated from one to another

kinetic formulation for systems of two conservation laws and elastodynamics for scalar conservation laws the kinetic formulation makes it possible to generate all the entropies from a simple kernel we show how this concept replaces and simplifies greatly the concept of young measures avoiding the difficulties encountered when working in lp the general construction of the two kinetic functions that generate the entropies of 2 2 strictly hyperbolic systems is also developed here we show that it amounts to building a universal entropy i e one that can be truncated by a kinetic value along riemann invariants for elastodynamics this construction can be completed and specialized using the additional galilean invariance this allows a full characterization of convex entropies it yields a kinetic formulation consisting of two semi kinetic equations which as usual are equivalent to the infinite family of all the entropy inequalities

global structure stability of riemann solutions of quasilinear hyperbolic systems of conservation laws shocks and contact discontinuities abstract in this paper the author proves the global structure stability of the lax s riemann solution u u x t containing only shocks and contact discontinuities of general n n quasilinear hyperbolic system of conservation laws more precisely the author proves the global existence and uniqueness of the piecewise c1 solution u u t x of a class of generalized riemann problem which can be regarded as a perturbation of the corresponding riemann problem for the quasilinear hyperbolic system of conservation laws moreover this solution has a global structure similar to that of the solution u u x t combining the results in kong global structure instability of riemann solutions of quasilinear hyperbolic systems of conservation laws rarefaction waves to appear the author proves that the lax s riemann solution of general n n quasilinear hyperbolic system of conservation laws is globally structurally stable if and only if it contains only non degenerate shocks and contact discontinuities but no rarefaction waves and other weak discontinuities

computing the lattice of all fixpoints of a fuzzy closure operator we present a fast bottom up algorithm to compute all fixpoints of a fuzzy closure operator in a finite set over a finite chain of truth degrees along with the partial order on the set of all fixpoints fuzzy closure operators appear in several areas of fuzzy logic and its applications including formal concept analysis fca that we use as a reference area of application in this paper several problems in fca such as computing all formal concepts from data with graded attributes or computing non redundant bases of all attribute dependencies can be reduced to the problem of computing fixpoints of particular fuzzy closure operators associated with the input data the development of a general algorithm that is applicable in particular to these problems is the ultimate purpose of this paper we present the algorithm its theoretical foundations and experimental evaluation

generalized solutions of the radiative transfer equations in a singular case this paper is devoted to the study of the radiative transfer equations first we prove a global existence theorem which allows a blow up of the opacity v when 0 thus it extends mercier s previous result 13 this proof relies mainly on a nonlinear version of hille yosida theorem see crandall ligett 9 then we prove the uniqueness of the semigroup solving tr and some regularity results in the class of functions with bounded variation finally we prove the convergence of some splitting algorithms associated to tr

a smooth transition model between kinetic and hydrodynamic equations this paper presents a model which provides a smooth transition between a kinetic and a hydrodynamic domain the idea is to use a buffer zone in which both hydrodynamics and kinetic equations will be solved the solution of the original kinetic equation will be recovered as the sum of the solutions of these two equations we use an artificial connecting function which makes the equation on each domain degenerate at the end of the buffer zone thus no boundary condition is needed at the transition point consequently this model avoids the delicate issue of finding the interface condition in a typical domain decomposition method that couples a kinetic equation with hydrodynamic equations a simple kinetic scheme is developed to discretize our model and numerical examples are used to validate the method

conditions for the existence of the least solution and minimal solutions to fuzzy relation equations over complete brouwerian lattices this paper discusses properties and existence conditions of minimal solutions to sup inf fuzzy relation equations over complete brouwerian lattices the relationship between minimal solutions to a system of fuzzy relation equations and minimal solutions to a fuzzy relation equation in the system is illustrated by two examples necessary and sufficient conditions for the existence of the least solution and minimal solutions to a system of fuzzy relation equations are given

global solutions to one dimensional shallow water magnetohydrodynamic equations abstract in this paper we study the cauchy problem for the one dimensional shallow water magnetohydrodynamic equations the main difficulty is the case of zero depth h 0 since the nonlinear flux function p h is singular and the definition of solution is not clear near h 0 first assuming that h has a positive and lower bound we establish the pointwise convergence of the viscosity solutions by using the div curl lemma from the compensated compactness theory to special pairs of functions c f e and obtain a global weak entropy solution second under some technical conditions on the initial data such that the riemann invariants w z are monotonic and increasing we introduce a variant of the vanishing artificial viscosity to select a weak solution finally we extend the results to two special cases where p h is for the polytropic gas or for the chaplygin gas

existence of solutions to hyperbolic conservation laws with a source existence of solutions to three different systems of eqs 1 1 1 2 and 1 3 coming from physically relevant models is shown each needing a different proof which are given in sects 2 3 and 4 the unifying theme is the presence of source terms and the general method of proof is vanishing viscosity together with compensated compactness for system 1 2 entropy entropy flux pairs of lax type are constructed and estimates from singular perturbation theory of odes are used for 1 1 and 1 3 weak entropy entropy flux pairs are constructed following the compensated compactness framework set up by diperna 4

fuzzy function as an approximate solution to a system of fuzzy relation equations this paper is mostly focused on the problem of approximate solvability of a system of fuzzy relation equations however we put a new light on this problem connecting it with the interpolation of a fuzzy function we introduce a notion of fuzzy function and its representation by fuzzy relation we demonstrate how problems of interpolation and approximation of fuzzy functions are connected with solvability of systems of fuzzy relation equations first we explain the general framework and then we prove some results related to the problem of the best approximation in particular we have shown that fuzzy relations introduced by sanchez and mamdani are the best approximations in certain approximation spaces

decay of entropy solutions of nonlinear conservation laws we are concerned with the asymptotic behavior of entropy solutions of nonlinear conservation laws the main objective of this paper is to present an analytical approach and to explore its applications to studying the large time behavior of periodic entropy solutions of hyperbolic conservation laws the asymptotic decay of periodic solutions of nonlinear hyperbolic conservation laws is an important nonlinear phenomenon it is observed that the genuine nonlinearity of equations forces the waves of each characteristic family to interact vigorously and to cancel each other the insightful analysis of glimm lax gl for scalar equations and 2 2 systems has indicated that the resultant mutual cancellation of interacting shock and rarefaction waves of the same family induces the decay of periodic solutions such a result was first shown by lax l1 in 1957 for one dimensional convex scalar conservation laws dafermos d1 applying his uniform processes proved the decay result for the case that the set of inflection points of the flux does not have an accumulation point the glimm lax theory gl indicates that for 2 2 strictly hyperbolic and genuinely nonlinear systems any periodic glimm solution decays like o 1 t this result was proved by using the approximate characteristic method in the glimm difference solutions provided that the oscillation of the corresponding initial data is small recently using the method of generalized characteristics dafermos d3 showed that any periodic solution with local bounded variation and small oscillation for 2 2 systems decays asymptotically with the same detailed structure pas found by lax l1 for the

attribute selection with fuzzy decision reducts rough set theory provides a methodology for data analysis based on the approximation of concepts in information systems it revolves around the notion of discernibility the ability to distinguish between objects based on their attribute values it allows to infer data dependencies that are useful in the fields of feature selection and decision model construction in many cases however it is more natural and more effective to consider a gradual notion of discernibility therefore within the context of fuzzy rough set theory we present a generalization of the classical rough set framework for data based attribute selection and reduction using fuzzy tolerance relations the paper unifies existing work in this direction and introduces the concept of fuzzy decision reducts dependent on an increasing attribute subset measure experimental results demonstrate the potential of fuzzy decision reducts to discover shorter attribute subsets leading to decision models with a better coverage and with comparable or even higher accuracy

isometric immersions of surfaces with two classes of metrics and negative gauss curvature the isometric immersion of two dimensional riemannian manifolds or surfaces with negative gauss curvature into the three dimensional euclidean space is studied in this paper the global weak solutions to the gauss codazzi equations with large data in l infty are obtained through the vanishing viscosity method and the compensated compactness framework the l infty uniform estimate and h 1 compactness are established through a transformation of state variables and construction of proper invariant regions for two types of given metrics including the catenoid type and the helicoid type the global weak solutions in l infty to the gauss codazzi equations yield the c1 1 isometric immersions of surfaces with the given metrics

lp solutions to the cauchy problem of the bgk equation the bgk model of the boltzmann equation plays an important role in the kinetic theory of rarefied gases some existence and uniqueness results of solutions to its cauchy problem were established for large initial data under various circumstances see for example perthame b global existence to the bgk model of boltzmann equation j differ equations 82 191 205 1989 in this paper by establishing some weighted lp estimates of the hydrodynamical quantities of a gas we prove the existence theorem of the lp solutions to the cauchy problem and establish the propagation properties of the lp moments for this kind of solutions

regularity of the moments of the solution of a transport equation let u u x v satisfy the transport equation u v xu f x rn v rnwhere f belongs to some space of type lp dx d v where is a positive bounded measure on rn we study the resulting regularity of the moment u x v d v in terms of fractional sobolev spaces for example counter examples are given in order to test the optimality of our results

cauchy problem for an isentropic magnetogasdynamic system abstract this paper investigates the cauchy problem for an isentropic magnetogasdynamic system under certain reasonable hypotheses on the initial data we obtain the global existence and uniqueness of the c 1 solution to the system meanwhile when the hypotheses on the initial data do not hold we obtain the blow up phenomena of the c 1 solution to the system the bounds of the solution are shown to depend on the parameter which characterizes a one dimensional plane flow 0 or a three dimensional cylindrically symmetric flow 1 it is shown that the existence of the finite time singularity is significantly influenced by the magnetic field strength present in the flow along with the initial data

attribute reduction in multi adjoint concept lattices knowledge reduction is one of the key issues in formal concept analysis and there have been many studies on this topic the irreducible elements in a lattice are also very important since they form the basic information of a relational system moreover they are also important from the viewpoint of attribute reduction both topics are notably more complicated in a fuzzy setting since not only the size of the sets of attributes and objects influence the size of the fuzzy concept lattice but the truth value sets where the sets of objects attributes and the relation are evaluated are important this paper presents in the general fuzzy framework of multi adjoint concept lattices a characterization of the meet irreducible elements from which a classification of attributes and its application to attribute reduction is introduced