a bgk type flux vector splitting scheme for the ultrarelativistic euler equations a gas kinetic solver is developed for the ultrarelativistic euler equations the scheme is based on the direct splitting of the flux function of the euler equations with inclusion of particle collisions in the transport process consequently the artificial dissipation in the new scheme is much reduced in comparison with the usual kinetic flux vector splitting kfvs schemes which are based on the free particle transport at the cell interfaces in the gas evolution stage although in a usual kfvs scheme the free particle transport gives robust solutions it gives a smeared solution at the contact discontinuities the new bgk type kfvs scheme solves this problem and gives robust and reliable solutions as well as good resolution at the contact discontinuity in contrast to the classical kinetic theory we have only a finite domain of dependence due to the structure of the light cone the scheme is naturally multidimensional and is extended to the two dimensional case in a usual dimensionally split manner that is the formulae for the fluxes can be used along each coordinate direction the high order resolution of the scheme is achieved by using a muscl type initial reconstruction in the numerical case studies the results obtained from the bgk type kfvs schemes are compared with the exact riemann solution kfvs schemes upwind schemes and central schemes

decay property for second order hyperbolic systems of viscoelastic materials we study a class of second order hyperbolic systems with dissipation which describes viscoelastic materials the considered dissipation is given by the sum of the memory term and the damping term when the dissipation is effective over the whole system we show that the solution decays in l 2 at the rate t n 4 as t provided that the corresponding initial data are in l 2 l 1 w heren is the space dimension the proof is based on the energy method in the fourier space also we discuss similar systems with weaker dissipation by introducing the operator 1 2 with 0 in front of the dissipation terms and

the timoshenko system with history and cattaneo law in this paper we study a fully hyperbolic thermoelastic timoshenko system with past history where the thermal effects are given by cattaneo s law we obtain exponential stability of solutions if and only if a new condition on the wave speed of propagation is verified otherwise when that condition fails we obtain polynomial stability of solutions in this case optimal rates of decay are established

general decay of solutions of a viscoelastic equation abstract in this paper we consider the following viscoelastic equation u t t u 0 t g t u d 0 in a bounded domain and establish a general decay result which is not necessarily of exponential or polynomial type this work generalizes and improves earlier results in the literature

energy decay for timoshenko systems of memory type abstract linear systems of timoshenko type equations for beams including a memory term are studied the exponential decay is proved for exponential kernels while polynomial kernels are shown to lead to a polynomial decay the optimality of the results is also investigated

exponential stability of laminated timoshenko beams with boundary internal controls abstract for a laminated timoshenko system with slip along the interface we study existence and boundary interior stabilization of solutions our first main result using resolvent estimates in the frequency domain is to show that interior damping created by the interfacial slip in companion with boundary feedback controls acting on the complementary displacements traverse and rotation angle drives the solution to zero with exponential decay rate we impose neither conditions on the physical parameters of the model nor on the damping coefficients our second main result is to investigate the asymptotic behavior of solutions for partially dissipative problems assuming the condition that the waves travel at the same speed we prove the decay of solutions with exponential rate finally the same condition allows us to show that dissipative effect created by the interfacial slip is strong enough to exponentially stabilizes the solutions to zero

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

decision combination in multiple classifier systems a multiple classifier system is a powerful solution to difficult pattern recognition problems involving large class sets and noisy input because it allows simultaneous use of arbitrary feature descriptors and classification procedures decisions by the classifiers can be represented as rankings of classifiers and different instances of a problem the rankings can be combined by methods that either reduce or rerank a given set of classes an intersection method and union method are proposed for class set reduction three methods based on the highest rank the borda count and logistic regression are proposed for class set reranking these methods have been tested in applications of degraded machine printed characters and works from large lexicons resulting in substantial improvement in overall correctness

boundary control of the timoshenko beam it is shown that the timoshenko beam can be uniformly stabilized by means of a boundary control a numerical study on the spectrum is also presented

stability theory for semigroups using l p l q fourier multipliers abstract we study polynomial and exponential stability for c 0 semigroups using the recently developed theory of operator valued l p l q fourier multipliers we characterize polynomial decay of orbits of a c 0 semigroup in terms of the l p l q fourier multiplier properties of its resolvent using this characterization we derive new polynomial decay rates which depend on the geometry of the underlying space we do not assume that the semigroup is uniformly bounded our results depend only on spectral properties of the generator as a corollary of our work on polynomial stability we reprove and unify various existing results on exponential stability and we also obtain a new theorem on exponential stability for positive semigroups

analysis of decision boundaries in linearly combined neural classifiers combining or integrating the outputs of several pattern classifiers has led to improved performance in a multitude of applications this paper provides an analytical framework to quantify the improvements in classification results due to combining we show that combining networks linearly in output space reduces the variance of the actual decision region boundaries around the optimum boundary this result is valid under the assumption that the a posteriori probability distributions for each class are locally monotonic around the bayes optimum boundary in the absence of classifier bias the error is shown to be proportional to the boundary variance resulting in a simple expression for error rate improvements in the presence of bias the error reduction expressed in terms of a bias reduction factor is shown to be less than or equal to the reduction obtained in the absence of bias the analysis presented here facilitates the understanding of the relationships among error rates classifier boundary distributions and combining in output space

global existence and optimal decay rates for the timoshenko system the case of equal wave speeds abstract we first show the global existence and optimal decay rates of solutions to the classical timoshenko system in the framework of besov spaces due to the non symmetric dissipation the general theory for dissipative hyperbolic systems see 31 cannot be applied to the timoshenko system directly in the case of equal wave speeds we construct global solutions to the cauchy problem pertaining to data in the spatially besov spaces furthermore the dissipative structure enables us to give a new decay framework which pays less attention on the traditional spectral analysis consequently the optimal decay estimates of solution and its derivatives of fractional order are shown by time weighted energy approaches in terms of low frequency and high frequency decompositions as a by product the usual decay estimate of l 1 r l 2 r type is also shown

a general decay result for a memory type timoshenko thermoelasticity system with second sound abstract in this paper we consider a system of timoshenko thermoelasticity with second sound in the presence of an infinite history term we prove under suitable conditions on the coefficients and the relaxation function a general decay result from which the exponential and polynomial decay estimates are only special cases we also establish a lack of exponential decay result and discuss the optimality for some situation

the stability number of the timoshenko system with second sound abstract in this work we consider the timoshenko beam model with second sound we introduce a new number 0 that characterizes the exponential decay we prove that the corresponding semigroup associated to the system is exponentially stable if and only if 0 0 otherwise there is a lack of exponential stability in this case we prove that the semigroup decays as t 1 2 moreover we show that the rate is optimal

on timoshenko type systems with type iii thermoelasticity asymptotic behavior abstract in this study we consider a thermoelastic beam system where the oscillations are defined by the timoshenko model and heat conduction is given by the green and naghdi theories we provide an explicit characterization of the decay rate which can be exponential or polynomial depending on the relationship between the coefficients of the wave propagation speed

a statistical unified framework for rank based multiple classifier decision combination abstract this study presents a theoretical investigation of the rank based multiple classifier decision combination problem with the aim of providing a unified framework to understand a variety of such systems the combination of the decisions of more than one classifiers with the aim of improving overall system performance is a concept of general interest in pattern recognition as a viable alternative to designing a single sophisticated classifier the problem of combining the classifier decisions in the raw form of candidate class rankings is formulated as a discrete optimization problem the objective function to be maximized is selected as the overall probability of correct decision this formulation introduces a set of observation statistics about the joint behavior of the classifiers which are to be estimated by observing the classifiers operated on a cross validation test set the resulting binary programming problem is shown to have a simple and global optimum solution but which also necessitates a prohibitive number of observation statistics from the objective function expansion the problem observation space is defined and a method based on partitioning is introduced to reduce its prohibitive dimensionality within this partitioning formalism called as the partitioned observation space pos theory the number of behavior observation statistics can be reduced to levels which are feasible to estimate from the available cross validation test data it is shown by examples that such specific partitionings can be defined when reasonable assumptions or prior knowledge about the classifiers are incorporated into the problem domain it is also demonstrated that certain specific partitionings of the classifier observation space effectively lead to the highest rank borda count and logistic regression rank based decision combination methods from the literature the analysis presented is general and promises to lead to a class of algorithms for rank based decision combination the potential of the theory and practical issues in implementation are illustrated by applying it in a real life phonetic discrimination problem from speech pattern classification with encouraging results

heat wave interaction in 2 3 dimensions optimal rational decay rate abstract in this paper we consider a simplified version of a fluid structure pde model which has been of longstanding interest within the mathematical and biological sciences in it a n dimensional heat equation replaces the original stokes system so as to ultimately have a vector valued heat equation and vector valued wave equation compose the coupled pde system under study the coupling between the two disparate pde components occurs across a boundary interface as such the entire pde dynamics manifests features of both hyperbolicity and parabolicity for this heat structure system our main result of uniform stability is as follows given smooth initial data i e data in the domain of the underlying semigroup generator of the coupled pde system the corresponding solutions decay at the rate of o t 1 this establishes the long conjectured optimal rate the problem of obtaining sharp rational decay rates for the heat wave pde under present consideration has been a much considered problem with the modus operandi of earlier efforts taking place within the time domain by contrast we adopt here a frequency domain approach which is based upon a recent resolvent criterion and which was initiated in our prior effort wherein we obtained the rate of decay o 1 t the present optimal improvement o t 1 is achieved by employing an additional tool in our analysis a microlocal analysis argument to estimate a critical term involving two problematic boundary traces

on the uniform decay in viscoelastic problems in rn in this paper we consider a linear cauchy viscoelastic problem we show that for compactly supported initial data and for an exponentially decaying relaxation function the decay of the first energy of solution is polynomial the finite speed propagation is used to compensate for the lack of poincare s inequality in r n

general stability result for viscoelastic wave equations in this paper we consider a viscoelastic equation and establish an explicit and general decay rate result without imposing restrictive assumptions on the behavior of the relaxation function at infinity our result allows a wider class of relaxation functions and improves earlier results in the literature

on convexity for energy decay rates of a viscoelastic equation with boundary feedback abstract in this paper we consider a viscoelastic equation with a nonlinear feedback localized on a part of the boundary we establish an explicit and general decay rate result using some properties of the convex functions our result is obtained without imposing any restrictive growth assumption on the damping term and strongly weakening the usual assumptions on the relaxation function

on the stability of timoshenko systems with gurtin pipkin thermal law abstract we analyze the differential system 1 t t x x 0 2 t t b x x x x 0 3 t 1 0 g s x x t s d s t x 0 describing a timoshenko beam coupled with a temperature evolution of gurtin pipkin type a necessary and sufficient condition for exponential stability is established in terms of the structural parameters of the equations in particular we generalize previously known results on the fourier timoshenko and the cattaneo timoshenko beam models

subspace ensembles for classification abstract ensemble learning constitutes one of the principal current directions in machine learning and data mining in this paper we explore subspace ensembles for classification by manipulating different feature subspaces commencing with the nature of ensemble efficacy we probe into the microcosmic meaning of ensemble diversity and propose to use region partitioning and region weighting to implement effective subspace ensembles individual classifiers possessing eminent performance on a partitioned region reflected by high neighborhood accuracies are deemed to contribute largely to this region and are assigned large weights in determining the labels of instances in this area a robust algorithm sena that incarnates the mechanism is presented which is insensitive to the number of nearest neighbors chosen to calculate neighborhood accuracies the algorithm exhibits improved performance over the well known ensembles of bagging adaboost and random subspace the difference of its effectivity with varying base classifiers is also investigated

mildly dissipative nonlinear timoshenko systems global existence and exponential stability we consider nonlinear systems of timoshenko type in a one dimensional bounded domain the system has a dissipative mechanism being present only in the equation for the rotation angle it is a damping effect through heat conduction the global existence of small smooth solutions as well as the exponential stability are investigated

boundary stabilization of solutions of a nonlinear system of timoshenko type in this paper we are concerned with a multidimensional timoshenko system subjected to boundary conditions of memory type we establish general rate decay results the usual exponential and polynomial decay rates are only special cases

feedback stabilization of rotating timoshenko beam with adaptive gain the problem of boundary feedback stabilization of rotating timoshenko beam arising from control of flexible robot arms is studied in this paper first under gain adaptive direct strain feedback controls a counterexample is given to show that the corresponding closed loop system is not asymptotically stable which is contrary to traditional conjecture the counterexample given in this paper also exemplifies an interesting result certain two two order linear partial differential equations with five homogeneous boundary conditions have non trivial solutions then with an additional boundary feedback control the related energy of the closed loop system is proved to be strongly stable or more precisely the configuration of the beam can be exponentially stabilized with some suitable non linear boundary feedback controls with adaptive gain

existence of global strong solutions in critical spaces for barotropic viscous fluids this paper is dedicated to the study of viscous compressible barotropic fluids in dimension n 2 we address the question of the global existence of strong solutions for initial data close to a constant state having critical besov regularity first this article shows the recent results of charve and danchin arch ration mech anal 198 1 233 271 2010 and chen et al commun pure appl math 63 1173 1224 2010 with a new proof our result relies on a new a priori estimate for the velocity that we derive via the intermediary of the effective velocity which allows us to cancel out the coupling between the density and the velocity as in haspot well posedness in critical spaces for barotropic viscous fluids 2009 second we improve the results of charve and danchin 2010 and chen et al 2010 by adding as in charve and danchin 2010 some regularity on the initial data in low frequencies in this case we obtain global strong solutions for a class of large initial data which rely on the results of hoff arch rational mech anal 139 303 354 1997 hoff commun pure appl math 55 11 1365 1407 2002 and hoff j math fluid mech 7 3 315 338 2005 and those of charve and danchin 2010 and chen et al 2010 we conclude by generalizing these results for general viscosity coefficients

handwritten numerical recognition based on multiple algorithms abstract in this paper the authors combine two algorithms for application to the recognition of unconstrained isolated handwritten numerals the first algorithm employs a modified quadratic discriminant function utilizing direction sensitive spatial features of the numeral image the second algorithm utilizes features derived from the profile of the character in a structural configuration to recognize the numerals while both algorithms yield very low error rates the authors combine the two algorithms in different ways to study the best polling strategy and realize very low error rates 0 2 or less and rejection rates below 4

on the well posedness of the incompressible density dependent euler equations in the lp framework abstract the present paper is devoted to the study of the well posedness issue for the density dependent euler equations in the whole space we establish local in time results for the cauchy problem pertaining to data in the besov spaces embedded in the set of lipschitz functions including the borderline case b p 1 n p 1 r n a continuation criterion in the spirit of the celebrated one by beale kato and majda 1984 in 2 for the classical euler equations is also proved in contrast with the previous work dedicated to this system in the whole space our approach is not restricted to the l 2 framework or to small perturbations of a constant density state we just need the density to be bounded away from zero the key to that improvement is a new a priori estimate in besov spaces for an elliptic equation with nonconstant coefficients

boltzmann type schemes for gas dynamics and the entropy property let h be a convex function a boltzmann equation is built following the b g k model for which h is an entropy in the fluid limit the compressible euler equations are obtained with a convex entropy naturally associated to h the motivation is to define numerical boltzmann schemes with finite speed of propagation corresponding to an equilibrium density function with bounded support the classical scheme obtained with h f f log f is based on the equilibrium density function exp v 2 2 which has infinite support

decay estimate and asymptotic profile for a plate equation with memory abstract in this paper the initial value problem for a plate equation with a memory is considered under weaker assumptions on the memory function we obtain the decay estimates of solutions which is of the regularity loss type by applying the energy method in fourier space moreover if the memory kernel is an exponential function we derive the large time behavior and asymptotic profile of solutions in the one dimensional space by virtue of the technique of spectral analysis

second order accurate kinetic schemes for the ultra relativistic euler equations a second order accurate kinetic scheme for the numerical solution of the relativistic euler equations is presented these equations describe the flow of a perfect fluid in terms of the particle density n the spatial part of the four velocity u and the pressure p the kinetic scheme is based on the well known fact that the relativistic euler equations are the moments of the relativistic boltzmann equation of the kinetic theory of gases when the distribution function is a relativistic maxwellian the kinetic scheme consists of two phases the convection phase free flight and collision phase the velocity distribution function at the end of the free flight is the solution of the collisionless transport equation the collision phase instantaneously relaxes the distribution to the local maxwellian distribution the fluid dynamic variables of density velocity and internal energy are obtained as moments of the velocity distribution function at the end of the free flight phase the scheme presented here is an explicit method and unconditionally stable the conservation laws of mass momentum and energy as well as the entropy inequality are everywhere exactly satisfied by the solution of the kinetic scheme the scheme also satisfies positivity and l1 stability the scheme can be easily made into a total variation diminishing method for the distribution function through a suitable choice of the interpolation strategy in the numerical case studies the results obtained from the first and second order kinetic schemes are compared with the first and second order upwind and central schemes we also calculate the experimental order of convergence and numerical l1 stability of the scheme for smooth initial data

numerical hydrodynamics from gas kinetic theory a new high resolution numerical hydrodynamic scheme is developed from considerations of gas kinetic theory this boltzmann type scheme uses the particle distribution function and follows its evolution to evaluate the numerical fluxes the intrinsic multidimensional property in the evolution stage of gas distribution function distinguishes it from any other high order upwind scheme from approximate boltzmann equation the navier stokes equations can be derived and this new numerical method uses this advantage to approximate the solutions of the navier stokes equations where the advection and dissipation effects are coupled in the time dependent gas distribution function several well defined numerical test cases are presented in one and two dimensions and it is shown that the resolution in the numerical results is competitive with those of any of the current high resolution schemes without special treatment of the discontinuities for strong rarefaction waves our scheme gives better results in this thesis we try to separate clearly numerical and physical effects and we also give a concise explanation of the necessity of including numerical viscosities implicitly or explicitly in high resolution godunov type and central difference schemes even for the navier stokes equations the main part of this thesis will be published in two papers 27 and 45 in the journal of computational physics

on the stability of damped timoshenko systems cattaneo versus fourier law we consider hyperbolic timoshenko type vibrating systems that are coupled to a heat equation modeling an expectedly dissipative effect through heat conduction while exponential stability under the fourier law of heat conduction holds it turns out that the coupling via the cattaneo law does not yield an exponentially stable system this seems to be the first example that a removal of the paradox of infinite propagation speed inherent in fourier s law by changing to the cattaneo law causes a loss of the exponential stability property actually for systems with history the fourier law keeps the exponential stability known for the pure timoshenko system without heat conduction but introducing the cattaneo coupling even destroys this property

on the energy decay of the linear thermoelastic plate with memory abstract we analyze the longterm properties of a c 0 semigroup describing the solutions to a linear evolution system that models a thermoelastic thin plate with memory effects in the heat flux law under reasonably general assumptions on the memory kernel all single trajectories are shown to decay to zero in spite of that the semigroup is not exponentially stable

global existence and decay estimates for the solution of a nonlinear bresse system abstract our main focus in the present paper is to study the global existence and asymptotic behavior of a nonlinear version of the bresse system as it has been already proved in soufyane and said houari 2014 the linear version of this system is of regularity loss type this regularity loss creates difficulties when dealing with the nonlinear problem since the dissipative property of the problem becomes very weak in the high frequency region and as a result the classical energy method fails to overcome this difficulty following ide and kawashima 2008 and ikehata 2002 we use an energy method with negative weights to create an artificial damping which allows us to control the nonlinearity

global existence and asymptotic decay of solutions to the nonlinear timoshenko system with memory abstract in this paper we consider the initial value problem for the nonlinear timoshenko system with a memory term due to the regularity loss property and weak dissipation we have to assume stronger nonlinearity than usual by virtue of the semi group arguments we obtain the global existence and optimal decay of solutions to the nonlinear problem under smallness and enough regularity assumptions on the initial data where we employ a time weighted l 2 energy method combined with the optimal l 2 decay of lower order derivatives of solutions

the frequency localization technique and minimal decay regularity for euler maxwell equations abstract dissipative hyperbolic systems of regularity loss have been recently received increasing attention extra higher regularity is usually assumed to obtain the optimal decay estimates in comparison with the global in time existence of solutions in this paper we develop a new frequency localization time decay property which enables us to overcome the technical difficulty and improve the minimal decay regularity for dissipative systems as an application it is shown that the optimal decay rate of l 1 r 3 l 2 r 3 is available for euler maxwell equations with the critical regularity s c 5 2 that is the extra higher regularity is not necessary

on the wellposedness of three dimensional inhomogeneous navier stokes equations in the critical spaces we prove the local wellposedness of three dimensional incompressible inhomogeneous navier stokes equations with initial data in the critical besov spaces without assumptions of small density variation furthermore if the initial velocity field is small enough in the critical besov space dot b 1 2 2 1 mathbb r 3 this system has a unique global solution

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

global existence asymptotic behavior and uniform attractors for a non autonomous timoshenko system of thermoelasticity of type iii with a time varying delay abstract in this paper we first establish the global existence by using the variable norm technique of kato and semigroup method second under suitable assumptions on the data we obtain the asymptotic behavior of the solution last we prove the existence of a uniform attractor by using the method of uniform contractive functions

global well posedness and polynomial decay for a nonlinear timoshenko cattaneo system under minimal sobolev regularity abstract we consider the nonlinear stability of the timoshenko cattaneo system in the one dimensional whole space the timoshenko system consists of two coupled wave equations with non symmetric relaxation and describes vibrations of the beam with shear deformation and rotational inertia effect generally if the relaxation is not symmetric the dissipation is produced through the complicated interaction of the components of the system and their decay estimates and the energy estimates are of regularity loss type in this paper we introduce the mathematical method to control such a weak dissipativity by investigating the timoshenko system with cattaneo s law which is the first order approximation of fourier s law with its time delay effect racke said houari 2012 showed the global existence and the decay estimate of solutions by assuming high regularity h 8 l 1 on the small initial data to control their weak dissipativity in contrast we prove the global existence in h 2 by energy methods without any negative weights our regularity assumption is the same as that needed to show the local existence that is we do not need to assume the extra higher regularity on the initial data besides the optimal decay estimate in h 2 l 1 is shown by using the time decay inequality of l p l q l r type

a new approach to the stability of an abstract system in the presence of infinite history abstract in this paper we consider the following problem u t t t a u t 0 g s a u t s d s 0 t 0 u t u 0 t t 0 u t 0 u 1 where a is a self adjoint positive definite operator and g is a positive nonincreasing function we adopt the method introduced in 19 for finite history with some modifications imposed by the nature of our problem to establish a general decay result which depends only on the behavior of the relaxation function our result extends the decay result obtained for problems with finite history to those with infinite history in addition it improves in some cases some decay results obtained earlier in 15

lower bounds for an integral involving fractional laplacians and the generalized navier stokes equations in besov spaces when estimating solutions of dissipative partial differential equations in l p related spaces we often need lower bounds for an integral involving the dissipative term if the dissipative term is given by the usual laplacian lower bounds can be derived through integration by parts and embedding inequalities however when the laplacian is replaced by the fractional laplacian the approach of integration by parts no longer applies in this paper we obtain lower bounds for the integral involving by combining pointwise inequalities for with bernstein s inequalities for fractional derivatives as an application of these lower bounds we establish the existence and uniqueness of solutions to the generalized navier stokes equations in besov spaces the generalized navier stokes equations are the equations resulting from replacing in the navier stokes equations by

an upwind kinetic flux vector splitting method on general mesh topologies an upwind flux vector splitting algorithm which utilizes the moments of the boltzmann equation to derive the euler equations for inviscid compressible flow has been used with a variety of grid types although the upwind approach offers the potential for accurate flow simulations it is necessary to ensure that such procedures can be utilized on realistic grids in this paper an upwind algorithm is used with structured multiblock grids unstructured grids of triangles and hybrid structured unstructured grids to solve realistic compressible flow problems in two dimensions

dissipative structure and global existence in critical space for timoshenko system of memory type abstract in this paper we consider the initial value problem for the timoshenko system with a memory term in one dimensional whole space in the first place we consider the linearized system applying the energy method in the fourier space we derive the pointwise estimate of the solution in the fourier space which first gives the optimal decay estimate of the solution next we give a characterization of the dissipative structure of the system by using the spectral analysis which confirms our pointwise estimate is optimal in the second place we consider the nonlinear system we show that the global in time existence and uniqueness result could be proved in the minimal regularity assumption in the critical sobolev space h 2 in the proof we don t need any time weighted norm as recent works we use just an energy method which is improved to overcome the difficulties caused by regularity loss property of timoshenko system

decay of solutions to an inertial model for a semilinear plate equation with memory abstract in this paper we focus on the initial value problem of an inertial model for a semilinear plate equation with memory in multi dimensions n 1 which is of regularity loss property by using fourier transform and laplace transform we obtain fundamental solutions to the corresponding linear problem and their pointwise estimates in the fourier space appealing to this pointwise estimates we obtain the global existence and the optimal decay estimates of solutions to the semilinear problem by employing the contraction mapping theorem

on output independence and complementariness in rank based multiple classifier decision systems this study presents a theoretical analysis of output independence and complementariness between classifiers in a rank based multiple classifier decision system in the context of the partitioned observation space theory to enable such an analysis an information theoretic interpretation of a rank based multiple classifier system is developed and basic concepts from information theory are applied to develop measures for output independence and complementariness it is shown that output independence of classifiers is not a requirement for achieving complementariness between these classifiers namely output independence does not imply a performance improvement by combining multiple classifiers a condition called dominance is shown to be important instead the information theoretic measures proposed for output independence and complementariness are justified by simulated examples

stabilization of the nonuniform timoshenko beam in this paper we consider a timoshenko beam with variable physical parameters we prove that the model can be stabilize by one control force for both internal and boundary cases

global solutions to the 3 d incompressible inhomogeneous navier stokes system in this paper we consider the global well posedness of the 3 d incompressible inhomogeneous navier stokes equations with initial data in the critical besov spaces a0 bq 13q r3 u0 u0h u03 bp 1 1 3p r3 for p q satisfying 1 q p 6 and 1q 1p 13 more precisely we prove that there exist two positive constants c0 c0 such that if a0 bq 13q u0h bp 1 1 3p exp c0 u03 bp 1 1 3p2 2 c0 then 1 3 has a unique global solution a l r bq 13q r3 u l r bp 1 1 3p r3 l1 r bp 11 3p r3 in particular this result implies the global well posedness result in abidi and paicu 2007 2 for the inhomogeneous navier stokes system with small initial data

note on intrinsic decay rates for abstract wave equations with memory in this paper we consider a viscoelastic abstract wave equation with memory kernel satisfying the inequality g h g 0 s 0 where h s is a given continuous positive increasing and convex function such that h 0 0 we shall develop an intrinsic method based on the main idea introduced by lasiecka and tataru uniform boundary stabilization of semilinear wave equation with nonlinear boundary dissipation differential and integral equations 6 507 533 1993 for determining decay rates of the energy given in terms of the function h s this will be accomplished by expressing the decay rates as a solution to a given nonlinear dissipative ode we shall show that the obtained result while generalizing previous results obtained in the literature is also capable of proving optimal decay rates for polynomially decaying memory kernels h s sp and for the full range of admissible parameters p 1 2 while such result has been known for certain restrictive ranges of the parameters p 1 3 2

decay rate estimates for a class of quasilinear hyperbolic equations with damping terms involving p laplacian in this paper we are concerned with the asymptotic behaviour of weak solutions to the initial boundary value problem for a class of quasilinear hyperbolic equations with damping terms involving p laplacian by using the multiplier methods we investigate the stability of weak solutions to the initial boundary value problem and obtain explicit decay rate estimation depending on strain caused stress term and damping terms

global attractors for a semilinear hyperbolic equation in viscoelasticity a semilinear partial differential equation of hyperbolic type with a convolution term describing simple viscoelastic materials with fading memory is considered regarding the past history memory of the displacement as a new variable the equation is transformed into a dynamical system in a suitable hilbert space the dissipation is extremely weak and it is all contained in the memory term longtime behavior of solutions is analyzed in particular in the autonomous case the existence of a global attractor for solutions is achieved

global existence and minimal decay regularity for the timoshenko system the case of non equal wave speeds abstract as a continued work of 18 we are concerned with the timoshenko system in the case of non equal wave speeds which admits the dissipative structure of regularity loss firstly with the modification of a priori estimates in 18 we construct global solutions to the timoshenko system pertaining to data in the besov space with the regularity s 3 2 owing to the weaker dissipative mechanism extra higher regularity than that for the global in time existence is usually imposed to obtain the optimal decay rates of classical solutions so it is almost impossible to obtain the optimal decay rates in the critical space to overcome the outstanding difficulty we develop a new frequency localization time decay inequality which captures the information related to the integrability at the high frequency part furthermore by the energy approach in terms of high frequency and low frequency decomposition we show the optimal decay rate for timoshenko system in critical besov spaces which improves previous works greatly

convergence to equilibrium of solutions to a nonautonomous semilinear viscoelastic equation with finite or infinite memory abstract in this paper we consider the nonautonomous semilinear viscoelastic equation u t t u 0 k s u t s d s f x u g t in r with dirichlet boundary conditions and finite t or infinite memory here is a bounded domain in r n with smooth boundary and the nonlinearity f r r is analytic in the second variable uniformly with respect to the first one for this equation we derive an appropriate lyapunov function and we use the ojasiewicz simon inequality to show that the dissipation given by the memory term is strong enough to prove the convergence to a steady state for any global bounded solution in addition we discuss the rate of convergence to equilibrium which is polynomial or exponential depending on the ojasiewicz exponent and the decay of the time dependent right hand side g

energy decay in a timoshenko type system of thermoelasticity of type iii in this paper we consider a one dimensional linear thermoelastic system of timoshenko type where the heat conduction is given by green and naghdi theories we prove the exponential stability by using the energy method

global existence in critical spaces for compressible navier stokes equations we investigate global strong solutions for isentropic compressible fluids with initial data close to a stable equilibrium we obtain the existence and uniqueness of a solution in a functional setting invariant by the scaling of the associated equations more precisely the initial velocity has the same critical regularity index as for the incompressible homogeneous navier stokes equations and one more derivative is needed for the density we point out a smoothing effect on the velocity and a l 1 decay on the difference between the density and the constant reference state the proof lies on uniform estimates for a mixed hyperbolic parabolic linear system with a convection term

wave equations with strong damping in hilbert spaces abstract we study the cauchy problem for abstract dissipative equations in hilbert spaces generalizing wave equations with strong damping terms in r n or exterior domains our main result is a generalized diffusion phenomenon the long time asymptotics of strongly damped wave equations is a combination of solutions of diffusion and wave equations in particular we obtain sharp decay estimates the proofs rely on the energy method in the fourier space and its generalization based on the spectral theorem for self adjoint operators

asymptotic behavior of the energy for a class of weakly dissipative second order systems with memory a class of second order abstract systems with memory and dirichlet boundary conditions is investigated by suitable liapunov functionals existence of solutions as well as asymptotic behavior are determined in particular when the memory kernel decays exponentially the polynomially decay of the solutions is proved

asymptotic stability of thermoelastic systems of bresse type abstract we provide a comprehensive stability analysis of the thermoelastic bresse system also known as the circular arch problem in particular assuming a temperature evolution of gurtin pipkin type we establish a necessary and sufficient condition for exponential stability in terms of the structural parameters of the problem as a byproduct a complete characterization of the longtime behavior of bresse type systems with fourier maxwell cattaneo and coleman gurtin thermal laws is obtained our main theorem also subsumes some recent achievements in the stability properties of thermoelastic timoshenko systems with classical and nonclassical heat conduction

global classical solutions for partially dissipative hyperbolic system of balance laws the basic existence theory of kato and majda enables us to obtain local in time classical solutions to generally quasilinear hyperbolic systems in the framework of sobolev spaces in x with higher regularity however it remains a challenging open problem whether classical solutions still preserve well posedness in the case of critical regularity this paper is concerned with partially dissipative hyperbolic system of balance laws under the entropy dissipative assumption we establish the local well posedness and blow up criterion of classical solutions in the framework of besov spaces with critical regularity with the aid of the standard iteration argument and friedrichs regularization method then we explore the theory of function spaces and develop an elementary fact that indicates the relation between homogeneous and inhomogeneous chemin lerner spaces mixed space time besov spaces this fact allows us to capture the dissipation rates generated from the partial dissipative source term and further obtain the global well posedness and stability by assuming at all times the shizuta kawashima algebraic condition as a direct application the corresponding well posedness and stability of classical solutions to the compressible euler equations with damping are also obtained

optimal polynomial decay of functions and operator semigroups we characterize the polynomial decay of orbits of hilbert space c 0 semigroups in resolvent terms we also show that results of the same type for general banach space semigroups and functions obtained recently in batty and duyckaerts j evol eq 8 765 780 2008 are sharp this settles a conjecture posed in batty and duyckaerts 2008

relaxation time limits of non isentropic hydrodynamic models for semiconductors abstract this work deals with non isentropic hydrodynamic models for semiconductors with short momentum and energy relaxation times the high and low frequency decomposition methods are used to construct uniform global classical solutions to cauchy problems of a scaled hydrodynamic model in the framework of critical besov spaces furthermore it is rigorously justified that the classical solutions strongly converge to that of a drift diffusion model as two relaxation times both tend to zero as a by product global existence of weak solutions to the drift diffusion model is also obtained

kinetic schemes for the ultra relativistic euler equations we present a kinetic numerical scheme for the relativistic euler equations which describe the flow of a perfect fluid in terms of the particle density n the spatial part of the four velocity u and the pressure p the kinetic approach is very simple in the ultra relativistic limit but may also be applied to more general cases the basic ingredients of the kinetic scheme are the phase density in equilibrium and the free flight the phase density generalizes the nonrelativistic maxwellian for a gas in local equilibrium the free flight is given by solutions of a collision free kinetic transport equation the scheme presented here is an explicit method and unconditionally stable we establish that the conservation laws of mass momentum and energy as well as the entropy inequality are everywhere exactly satisfied by the solution of the kinetic scheme for that reason we obtain weak admissible euler solutions including arbitrarily complicated shock interactions in the numerical case studies the results obtained from the kinetic scheme are compared with the first order upwind and centered schemes

general decay result for nonlinear viscoelastic equations abstract in this paper we consider a nonlinear viscoelastic equation with minimal conditions on the l 1 0 relaxation function g namely g t t h g t where h is an increasing and convex function near the origin and is a nonincreasing function with only these very general assumptions on the behavior of g at infinity we establish optimal explicit and general energy decay results from which we can recover the optimal exponential and polynomial rates when h s s p and p covers the full admissible range 1 2 we get the best decay rates expected under this level of generality and our new results substantially improve several earlier related results in the literature

kinetic symmetrizations and pressure laws for the euler equations abstract the symmetrizations of the compressible euler equations written as kinetic mean are studied some of their properties are pointed out we emphasize for numerical purpose the case of real rarefied gases with pressure laws p f flux splitting formulae are derived for such pressure laws

new developments in kinetic schemes kinetic schemes for the numerical solution of pde of fluid dynamics are a new class of upwind schemes the moment method strategy used in constructing these schemes is based on the connection between the boltzmann equation of kinetic theory of gases and governing equations of fluid dynamics any upwind scheme for the solution of the boltzmann equation becomes an upwind scheme for the solution of pde of fluid dynamics by taking suitable moments this idea has been exploited in the present paper in developing least squares kinetic upwind method lskum and kinetic flux vector splitting method on moving grid kfmg the robustness and versatility of lskum has been demonstrated by applying it to 2 d flow problems of inviscid gas dynamics the lskum has been found to operate on any type of grid and can be called a grid fault tolerant scheme in view of the use of least squares approximation to the space derivatives the kfmg is a promising new method showing how easily the kinetic schemes lend themselves easily to problems involving moving grids which are generally employed while solving problems in unsteady aerodynamics