on the riemann problem for a system of balance laws modelling a reactive gas mixture abstract this paper deals with the riemann problem for a gas mixture undergoing reversible and irreversible bimolecular reactions governed by a suitable closure at euler level of the boltzmann equation which results to be a set of balance laws the aim of the paper is to investigate questions like compatibility with entropy principle and dissipative character of the system in order to better understand the effects of the source terms on the structure of the solution of the riemann problem and its relation with the corresponding solution in absence of chemical reactions which is here deduced explicitly numerical simulations show the space time evolution of the solution profiles for the proposed reactive system

singular perturbations of first order hyperbolic systems with stiff source terms abstract this work develops a singular perturbation theory for initial value problems of nonlinear first order hyperbolic systems with stiff source terms in several space variables it is observed that under reasonable assumptions many equations of classical physics of that type admit a structural stability condition this condition is equivalent to the well known subcharacteristic condition for one dimensional 2 2 systems and the well known time like condition for one dimensional scalar second order hyperbolic equations with a small positive parameter multiplying the highest derivatives under this stability condition we construct formal asymptotic approximations of the initial layer solution to the nonlinear problem furthermore assuming some regularity of the solutions to the limiting inner problem and the reduced problem we prove the existence of classical solutions in the uniform time interval where the reduced problem has a smooth solution and justify the validity of the formal approximations in any fixed compact subset of the uniform time interval the stability condition seems to be a key to problems of this kind and can be easily verified moreover this presentation unifies and improves earlier works for some specific equations

thermal non equilibrium flows in three space dimensions we study the equations describing the motion of a thermal non equilibrium gas in three space dimensions it is a hyperbolic system of six equations with a relaxation term the dissipation mechanism induced by the relaxation is weak in the sense that the shizuta kawashima criterion is violated this implies that a perturbation of a constant equilibrium state consists of two parts one decays in time while the other stays in fact the entropy wave grows weakly along the particle path as the process is irreversible we study thermal properties related to the well posedness of the nonlinear system we also obtain a detailed pointwise estimate on the green s function for the cauchy problem when the system is linearized around an equilibrium constant state the green s function provides a complete picture of the wave pattern with an exact and explicit leading term comparing with existing results for one dimensional flows our results reveal a new feature of three dimensional flows not only does the entropy wave not decay but the velocity also contains a non decaying part strongly coupled with its decaying one the new feature is supported by the second order approximation via the chapman enskog expansions which are the navier stokes equations with vanished shear viscosity and heat conductivity

frequency localization duhamel principle and its application to the optimal decay of dissipative systems in low dimensions abstract recently a time decay framework l 2 r n b 2 s r n s 0 has been given by 49 for linearized dissipative hyperbolic systems which allows to pay less attention to the traditional spectral analysis however owing to interpolation techniques those decay results for nonlinear hyperbolic systems hold true only in higher dimensions n 3 and the analysis in low dimensions say n 1 2 was left open we try to give a satisfactory answer in the current work first of all we develop new time decay properties on the frequency localization duhamel principle and then it is shown that the classical solution and its derivatives of fractional order decay at the optimal algebraic rate in dimensions n 1 2 by using a new technique which is the so called piecewise duhamel principle in localized time weighted energy approaches compared to 49 finally as direct applications explicit decay statements are worked out for some relevant examples subjected to the same dissipative structure for instance damped compressible euler equations the thermoelasticity with second sound and timoshenko systems with equal wave speeds

global quasi neutral limit of euler maxwell systems with velocity dissipation abstract we consider smooth solutions to the cauchy problem for an isentropic euler maxwell system with velocity dissipation and small physical parameters for initial data uniformly close to constant equilibrium states we prove the global in time convergence of the system as the parameters go to zero the limit systems are the e mhd system and the incompressible euler equations both with velocity dissipation the proof of the results relies on a single uniform energy estimate with respect to the time and the parameters together with compactness arguments for this purpose the classical energy estimates for the symmetrizable hyperbolic system are not sufficient we construct a lyapunov type energy by controlling the divergence and the curl of the velocity the electric and magnetic fields

bv solutions for hyperbolic systems of balance laws with relaxation abstract for hyperbolic systems of balance laws with source manifesting relaxation it is shown that the kawashima condition which yields global classical solutions with smooth initial values near equilibrium is also instrumental in inducing the existence of global admissible bv solutions accommodating shocks

gas dynamics in thermal nonequilibrium and general hyperbolic systems with relaxation we study gas flow in vibrational nonequilibrium the model is a 4 4 nonlinear hyperbolic system with relaxation under physical assumptions properties of thermodynamic variables relevant to stability are obtained global existence for cauchy problems with smooth and small data is established and large time behavior is studied in the pointwise sense we formulate the fundamental solution in a systematic way for a general linear system with relaxation the fundamental solution provides insights to the behavior of the nonlinear system and is crucial to obtain our pointwise asymptotic picture for the nonequilibrium flow we also clarify in a general setting the relation between subcharacteristic conditions and a dissipative criterion that was originally proposed for hyperbolic parabolic systems and has now proved to be important also for hyperbolic systems with relaxation

representation theory of 0 hecke clifford algebras abstract the representation theory of 0 hecke clifford algebras as a degenerate case is not semisimple and also with rich combinatorial meaning bergeron hivert and thibon have proved that the grothendieck ring of the category of finitely generated supermodules of 0 hecke clifford algebras is isomorphic to the algebra of peak quasisymmetric functions defined by stembridge in this paper we further study the category of finitely generated projective supermodules and clarify the correspondence between it and the peak algebra of symmetric groups in particular two kinds of restriction rules for induced projective supermodules are obtained after that we consider the corresponding heisenberg double and its fock representation to prove that the ring of peak quasisymmetric functions is free over its subring of symmetric functions spanned by schur s q functions

packing of regular tetrahedral quartets of circles on a sphere how must 4n nonoverlapping equal circles forming n quartets be packed on a sphere so that the angular diameter of the circles will be as large as possible under the constraint that within each qua

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

lyndon word decompositions and pseudo orbits on q nary graphs abstract a foundational result in the theory of lyndon words words that are strictly earlier in lexicographic order than their cyclic permutations is the chen fox lyndon theorem which states that every word has a unique non increasing decomposition into lyndon words this article extends this factorization theorem obtaining the proportion of these decompositions that are strictly decreasing this result is then used to count primitive pseudo orbits sets of primitive periodic orbits on q nary graphs as an application we obtain a diagonal approximation to the variance of the characteristic polynomial coefficients of q nary quantum graphs

hyperbolic compressible navier stokes equations abstract we consider the non isentropic compressible navier stokes equations with hyperbolic heat conduction and a law for the stress tensor which is modified correspondingly by maxwell s law these two relaxations turning the whole system into a hyperbolic one are not only treated simultaneously but are also considered in a version having galilean invariance for this more complicated relaxed system the global well posedness is proved for small data moreover for vanishing relaxation parameters the solutions are shown to converge to solutions of the classical system

global classical solutions to a kind of quasilinear hyperbolic systems in several space variables abstract for a kind of quasilinear hyperbolic systems in several space variables whose coefficient matrices commute each other by means of normalized coordinates formulas of wave decomposition and pointwise decay estimates the global existence of classical solution to the cauchy problem for small and decaying initial data is obtained under hypotheses of weak linear degeneracy and weakly strict hyperbolicity

analysis of non isentropic compressible euler equations with relaxation abstract this paper is contributed to the study of the one dimensional non isentropic compressible euler equations with relaxation it is shown that classical solutions do not exist globally in time under general conditions on initial data indeed finite time blowup occurs in a quantity related to the first moment on the other hand when the initial datum is sufficiently close to a constant equilibrium state it is shown that the equations possess a unique global in time classical solution and the solution converges to the equilibrium state in the long time run when the domain is finite the convergence rate is shown to be exponential due to boundary effects

construction of bgk models with a family of kinetic entropies for a given system of conservation laws we introduce a general framework for kinetic bgk models we assume to be given a system of hyperbolic conservation laws with a family of lax entropies and we characterize the bgk models that lead to this system in the hydrodynamic limit and that are compatible with the whole family of entropies this is obtained by a new characterization of maxwellians as entropy minimizers that can take into account the simultaneous minimization problems corresponding to the family of entropies we deduce a general procedure to construct such bgk models and we show how classical examples enter the framework we apply our theory to isentropic gas dynamics and full gas dynamics and in both cases we obtain new bgk models satisfying all entropy inequalities

hyperbolic conservation laws with stiff relaxation terms and entropy we study the limiting behavior of systems of hyperbolic conservation laws with stiff relaxation terms reduced systems inviscid and viscous local conservation laws and weakly nonlinear limits are derived through asymptotic expansions an entropy condition is introduced for n n systems that ensures the hyperbolicity of the reduced inviscid system the resulting characteristic speeds are shown to be interlaced with those of the original system moreover the first correction to the reduced system is shown to be dissipative a partial converse is proved for 2 2 systems this structure is then applied to study the convergence to the reduced dynamics for the 2 2 case 1994 john wiley sons inc

split hopf algebras quasi shuffle algebras and the cohomology of ωσx abstract let a and b be two connected graded commutative k algebras of finite type where k is a perfect field of positive characteristic p we prove that the quasi shuffle algebras generated by a and b are isomorphic as hopf algebras if and only if a and b are isomorphic as graded k vector spaces equipped with a frobenius pth power map for the hardest part of this analysis we work with the dual construction and are led to study connected graded cocommutative hopf algebras h with two additional properties h is free as an associative algebra and the projection onto the indecomposables is split as a morphism of graded k vector spaces equipped with a verschiebung map building on work on non commutative witt vectors by goerss lannes and morel we classify such free split hopf algebras a topological consequence is that if x is a based path connected space then the hopf algebra h x k is determined by the stable homotopy type of x we also discuss the much easier analogous characteristic 0 results and give a characterization of when our quasi shuffle algebras are polynomial generalizing the so called ditters conjecture

uniform global existence and parabolic limit for partially dissipative hyperbolic systems abstract this work concerns smooth solutions to the cauchy problem for first order partially dissipative hyperbolic systems with a small parameter the systems are written in non conservative form in several space variables we introduce algebraic conditions on the structure of the systems under these conditions together with a partial dissipation condition and the shizuta kawashima stability condition we prove three main results around constant equilibrium states these results are uniform global existence with respect to the parameter global in time convergence of the systems to second order nonlinear parabolic systems in a slow time variable and global existence when the parameter is fixed we also give examples of physical models to which the above results can be applied

existence of traveling wave solutions for hyperbolic systems of balance laws this paper is concerned with traveling wave solutions for hyperbolic systems of balance laws satisfying a stability condition and a kawashima like condition we are interested in the case where the traveling wave equations have a singularity which is absent for 2 2 systems satisfying the two conditions to deal with the singularity we reduce the problem to a parametrized one without singularity by using the center manifold theorem for the parametrized problem we prove the existence of solutions by modifying an existing argument in the literature in this way we show the existence of traveling wave solutions

large time asymptotics for partially dissipative hyperbolic systems this work is concerned with n component hyperbolic systems of balance laws in m space dimensions first we consider linear systems with constant coefficients and analyze the possible behavior of solutions as t using the fourier transform we examine the role that control theoretical tools such as the classical kalman rank condition play we build lyapunov functionals allowing us to establish explicit decay rates depending on the frequency variable in this way we extend the previous analysis by shizuta and kawashima under the so called algebraic condition sk in particular we show the existence of systems exhibiting more complex behavior than the one that the sk condition allows we also discuss links between this analysis and previous literature in the context of damped wave equations hypoellipticity and hypocoercivity to conclude we analyze the existence of global solutions around constant equilibria for nonlinear systems of balance laws our analysis of the linear case allows proving existence results in situations that the previously existing theory does not cover

existence of relaxation shock profiles for hyperbolic conservation laws in this paper we prove that like viscosity relaxation can also smooth weak shocks for strict hyperbolic conservation laws as equilibium systems of hyperbolic relaxation systems under some natural structural conditions these conditions were derived previously by yong from stability considerations and hence are entirely analogous to the majda pego criterion of the viscous case the proof involves a new parametrization of hugoniot curves and a delicate analysis of the algebraic structure of relaxation systems as well as construction of an appropriate center manifold

global existence of smooth solutions for partially dissipative hyperbolic systems with a convex entropy we consider the cauchy problem for a general one dimensional n n hyperbolic symmetrizable system of balance laws it is well known that in many physical examples for instance for the isentropic euler system with damping the dissipation due to the source term may prevent the shock formation at least for smooth and small initial data our main goal is to find a set of general and realistic sufficient conditions to guarantee the global existence of smooth solutions and possibly to investigate their asymptotic behavior for systems which are entropy dissipative a quite natural generalization of the kawashima condition for hyperbolic parabolic systems can be given in this paper we first propose a general framework for this kind of problem by using the so called entropy variables then we go on to prove some general statements about the global existence of smooth solutions under different sets of conditions in particular the present approach is suitable for dealing with most of the physical examples of systems with a relaxation extension our main tools will be some refined energy estimates and the use of a suitable version of the kawashima condition

dissipative structure and entropy for hyperbolic systems of balance laws in this paper we introduce an entropy condition for hyperbolic systems of balance laws under this condition we use the chapman enskog expansion to derive the corresponding viscous conservation laws further structural conditions are discussed in order to develop local and global existence theories for the balance laws and viscous conservation laws

relaxation time limit of the multidimensional bipolar hydrodynamic model in besov space abstract in this paper we study a multidimensional bipolar hydrodynamic model for semiconductors or plasmas this system takes the form of the bipolar euler poisson model with electric field and frictional damping added to the momentum equations in the framework of the besov space theory we establish the global existence of smooth solutions for cauchy problems when the initial data are sufficiently close to the constant equilibrium next based on the special structure of the nonlinear system we also show the uniform estimate of solutions with respect to the relaxation time by the high and low frequency decomposition methods finally we discuss the relaxation time limit by compact arguments that is it is shown that the scaled classical solution strongly converges towards that of the corresponding bipolar drift diffusion model as the relaxation time tends to zero

global solution to initial boundary value problem for gas dynamics in thermal nonequilibrium abstract the global existence and long time behavior of smooth solutions to an initial boundary value problem for the system of thermal nonequilibrium gas dynamics are studied in this paper

discrete kinetic schemes for multidimensional systems of conservation laws we present here some numerical schemes for general multidimensional systems of conservation laws based on a class of discrete kinetic approximations which includes the relaxation schemes by s jin and z xin these schemes have a simple formulation even in the multidimensional case and do not need the solution of the local riemann problems for these approximations we give a suitable multidimensional generalization of the whitham s stability subcharacteristic condition in the scalar multidimensional case we establish the rigorous convergence of the approximated solutions to the unique entropy solution of the equilibrium cauchy problem

asymptotic stability in a second order symmetric hyperbolic system modeling the relativistic dynamics of viscous heat conductive fluids with diffusion abstract this paper establishes nonlinear asymptotic stability of homogeneous reference states in dissipative relativistic fluid dynamics the result is a counterpart for general non barotropic fluids of one obtained by the author in a previous paper on barotropic fluids differently from that of this earlier finding the proof here crucially relies on analyzing the corresponding linearized problem in fourier space with different scalings for small and large wave numbers

the algebra of quasi symmetric functions is free over the integers let z denote the leibniz hopf algebra which also turns up as the solomon descent algebra and the algebra of noncommutative symmetric functions as an algebra z z z1 z2 the free associative algebra over the integers in countably many indeterminates the coalgebra structure is given by zn ni 0 zi zn i z0 1 let m be the graded dual of z this is the algebra of quasi symmetric functions the ditters conjecture says that this algebra is a free commutative algebra over the integers in this paper the ditters conjecture is proved

duality between quasi symmetrical functions and the solomon descent algebra abstract the ring qsym of quasi symmetric functions is naturally the dual of the solomon descent algebra the product and the two coproducts of the first extending those of the symmetric functions correspond to a coproduct and two products of the second which are defined by restriction from the symmetric group algebra a consequence is that qsym is a free commutative algebra

hyperbolic principal subsystems entropy convexity and subcharacteristic conditions we consider a system of n balance laws compatible with an entropy principle and convex entropy density using the special symmetric form induced by the main field we define the concept of principal subsystem associated with the system we prove that the 2 n 2 principal subsystems are also symmetric hyperbolic and satisfy a subentropy law moreover we can verify that for each principal subsystem the maximum minimum characteristic velocity is not larger smaller than the maximum minimum characteristic velocity of the full system these are the subcharacteristic conditions we present some simple examples in the case of the euler fluid then in the case of dissipative hyperbolic systems we consider an equilibrium principal subsystem and we discuss the consequences in the setting of extended thermodynamics finally in the moments approach to the boltzmann equation we prove as a consequence of the previous result that the maximum characteristic velocity evaluated at the equilibrium state does not decrease when the number of moments increases

moment closure hierarchies for kinetic theories this paper presents a systematicnonperturbative derivation of a hierarchy of closed systems of moment equations corresponding to any classical kinetic theory the first member of the hierarchy is the euler system which is based on maxwellian velocity distributions while the second member is based on nonisotropic gaussian velocity distributions the closure proceeds in two steps the first ensures that every member of the hierarchy is hyperbolic has an entropy and formally recovers the euler limit the second involves modifying the collisional terms so that members of the hierarchy beyound the second also recover the correct navier stokes behavior this is achieved through the introduction of a generalization of the bgk collision operator the simplest such system in three spatial dimensions is a 14 moment closure which also recovers the behavior of the grad 13 moment system when the velocity distributions lie near local maxwellians the closure procedure can be applied to a general class of kinetic theories

pointwise time asymptotic behavior of solutions to a general class of hyperbolic balance laws abstract in this paper we are interested in a general class of hyperbolic balance laws within the frame work of existence of a convex entropy function that symmetrizes the system in certain sense and the kawashima shizuta condition we study the large time behavior of the solution to the cauchy problem in one space dimension for a solution around a constant equilibrium state we predetermine the asymptotic solution as a superposition of the constant state and diffusion waves along the equilibrium characteristic directions we estimate the remainder in the pointwise sense both in space and in time the decay rates in various directions are optimal which further give the optimal l p rates with 1 p applications to several examples including the kerr debye model are given

quantum quasi symmetric functions and hecke algebras the algebra of quasi symmetric functions is known to describe the characters of the hecke algebra of type at v 0 we present a quantization of this algebra defined in terms of filtrations of induced representations of the 0 hecke algebra we show that this q deformed algebra admits a simple realization in terms of quantum polynomials for generic values of q the algebra of quantum quasi symmetric functions is isomorphic to the one of noncommutative symmetric functions this gives rise to a one parameter family of hilbert space structures on the algebra of noncommutative symmetric functions as well as to new interesting bases

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

l p l q decay estimates for dissipative linear hyperbolic systems in 1d abstract given a b r n n we consider the cauchy problem for partially dissipative hyperbolic systems having the form t u a x u b u 0 with the aim of providing a detailed description of the large time behavior sharp l p l q estimates for 1 q p are established for the distance between the solution to the system and a time asymptotic profile where the profile is the superposition of diffusion waves and exponentially decaying waves they show that the solution to the system decays to the diffusion waves 1 2 faster than the diffusive decay rate 1 q 1 p 2 while the exponential decaying waves are negligible for large time in particular under a symmetry property it decays 1 faster than the proof is based on a complex interpolation argument once l r estimates for the fundamental solution to the system in the frequency space and fourier multiplier estimates are accomplished

maximum entropy principle for rarefied polyatomic gases in this chapter we prove in the case of polyatomic rarefied gases that the maximum entropy principle mep gives the same closure of the system as that obtained in the phenomenological et theory with 14 fields discussed in chap 5 the main idea is to consider a generalized distribution function depending not only on the velocity but also on an extra variable that connects with the internal degrees of freedom of a constituent molecule on the basis of mep we again obtain the same binary hierarchy introduced in the previous chapter the one is the usual momentum type f series and the other is the energy type g series the extra variable plays a role in the g series thus we prove the perfect agreement between the et theory and the molecular et theory at least within 14 field theories the agreement for any number of moments will be proved in chap 10

global existence for small data of the viscous green naghdi type equations abstract we consider the cauchy problem for the green naghdi equations with viscosity for small initial data it is well known that adding a second order dissipative term to a hyperbolic system leads to the existence of global smooth solutions once the hyperbolic system is symmetrizable and the so called kawashima shizuta condition is satisfied in a previous work we have proved that the green naghdi equations can be written in a symmetric form using the associated hamiltonian this system being dispersive in the sense that it involves third order derivatives the symmetric form is based on symmetric differential operators in this paper we use this structure for an appropriate change of variable to prove that adding viscosity effects through a second order term leads to global existence of smooth solutions for small data we also deduce that constant solutions are asymptotically stable

the algebra of multitangent functions abstract multizeta values are numbers appearing in many different contexts unfortunately their arithmetics remains mostly out of reach in this article we define a functional analogue of the algebra of multizeta values namely the algebra of multitangent functions which are 1 periodic functions defined by a process formally similar to multizeta values we introduce here the fundamental notions of reduction into monotangent functions projection onto multitangent functions and that of trifactorization giving a way of writing a multitangent function in terms of hurwitz multizeta functions this explains why the multitangent algebra is a functional analogue of the algebra of multizeta values we then discuss the most important algebraic and analytic properties of these functions and their consequences on multizeta values as well as their regularization in the divergent case each property of multitangents has a pendant on the side of multizeta values this allows us to propose new conjectures which have been checked up to the weight 18

entropy and global existence for hyperbolic balance laws this paper presents a general result on the existence of global smooth solutions to hyperbolic systems of balance laws in several space variables we propose an entropy dissipation condition and prove the existence of global smooth solutions under initial data close to a constant equilibrium state in addition we show that a system of balance laws satisfies a kawashima condition if and only if its first order approximation namely the hyperbolic parabolic system derived through the chapman enskog expansion satisfies the corresponding kawashima condition the result is then applied to bouchut s discrete velocity bgk models approximating hyperbolic systems of conservation laws

large time behavior of solutions for hyperbolic balance laws we study the existence and the large time behavior of global solutions to the initial value problem for hyperbolic balance laws in n space dimensions with n 3 admitting an entropy and satisfying the stable condition we first construct global existence of the solutions to such a system around a steady state if the initial energy is small enough then we show that k order derivatives of these solutions approach a constant state in the lp norm at a rate o t 12 k n2 np with p 2 and 0 n2 provided that initially z0 b 2 where b 2 is a homogeneous besov space these decay results do not impose an additional smallness assumption on lp norm of the initial data and we thus improve the results in 3 19 we also show faster decay results in the sense that if pz0 b 2 i p z0 b 2 1 with n2 n 22 k order derivatives of the solutions approach a constant state in the lp norm at a rate o t 12 k 1 n2 np

suspension splittings and james hopf invariants james constructed a functorial homotopy decomposition x w1 n 1 x n for path connected pointed cw complexes x we generalize this to a functorial decomposition of a where a is any functorial retract of a looped co h space this is used to construct hopf invariants in a more general context in addition when a y is the loops on a co h space we show that the wedge summands of y further functorially decompose by using an action of an appropriate symmetric group