stationary waves for the discrete boltzmann equation in the half space with reflective boundaries the present paper is concerned with stationary solutions for discrete velocity models of the boltzmann equation with reflective boundary condition in the first half space we obtain a sufficient condition that guarantees the existence and the uniqueness of stationary solutions satisfying the reflective boundary condition as well as the spatially asymptotic condition given by a maxwellian state first the sufficient condition is obtained for the linearized system then this result is applied to prove the existence theorem for the nonlinear equation through the contraction mapping principle also it is shown that the stationary solution approaches the asymptotic maxwellian state exponentially as the spatial variable tends to infinity

on relaxation hyperbolic systems violating the shizuta kawashima condition in this paper we start a general study on relaxation hyperbolic systems which violate the shizuta kawashima sk coupling condition this investigation is motivated by the fact that this condition is not satisfied by various physical systems and almost all the time in several space dimensions first we explore the role of entropy functionals around equilibrium solutions which may not be constant proposing a stability condition for such solutions then we find strictly dissipative entropy functions for one dimensional 2 2 systems which violate the sk condition finally we prove the existence of global smooth solutions for a class of systems such that condition sk does not hold but which are linearly degenerated in the non dissipative directions

the strong relaxation limit of the multidimensional isothermal euler equations we construct global smooth solutions to the multidimensional isothermal euler equations with a strong relaxation when the relaxation time tends to zero we show that the density converges towards the solution to the heat equation

free vibration analysis of laminated orthotropic spherical shells abstract analytical solutions are presented for the free vibration of laminated orthotropic spherical shells the analysis is based on the application of the chebyshev galerkin spectral method for the evaluation of free vibration frequencies and mode shapes the eigenvalue problem is defined in terms of five equations of motion in terms of the meridional coordinate the circumference variation of the displacements being represented in a fourier series numerical results are presented to show the validity and accuracy of the proposed method results of parametric studies for laminated annular spherical shells with different orthotropic ratios opening angles lamination sequences and shear deformation are also presented

the boltzmann equation besov spaces and optimal time decay rates in rxn abstract we prove that k th order derivatives of perturbative classical solutions to the hard and soft potential boltzmann equation without the angular cut off assumption in the whole space r x n with n 3 converge in large time to the global maxwellian with the optimal decay rate of o t 1 2 k n 2 n r in the l x r l v 2 norm for any 2 r these results hold for any 0 n 2 as long as initially f 0 b 2 l v 2 in the hard potential case we prove faster decay results in the sense that if p f 0 b 2 l v 2 and i p f 0 b 2 1 l v 2 for n 2 n 2 2 then the solution decays the global maxwellian in l v 2 l x 2 with the optimal large time decay rate of o t 1 2

global solution and large time behavior of the 3d compressible euler equations with damping national natural science foundation of china nsaf 10976026 national natural science foundation of china 11271305

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

the optimal decay estimates on the framework of besov spaces for generally dissipative systems we give a new decay framework for the general dissipative hyperbolic system and the hyperbolic parabolic composite system which allows us to pay less attention to the traditional spectral analysis in comparison with previous efforts new ingredients lie in the high frequency and low frequency decomposition of a pseudo differential operator and an interpolation inequality related to homogeneous besov spaces of negative order furthermore we develop the littlewood paley pointwise energy estimates and new time weighted energy functionals to establish optimal decay estimates on the framework of spatially critical besov spaces for the degenerately dissipative hyperbolic system of balance laws based on the l p mathbb r n embedding and the improved gagliardo nirenberg inequality the optimal l p mathbb r n l 2 mathbb r n 1 leqq p 2 decay rates and l p mathbb r n l q mathbb r n 1 leqq p 2 leqq q leqq infty decay rates are further shown finally as a direct application the optimal decay rates for three dimensional damped compressible euler equations are also obtained

discrete velocity models of the boltzmann equation a survey on the mathematical aspects of the theory discrete velocity models of the boltzmann equation are of considerable conceptual interest in the kinetic theory of gases and at the same time a fascinating mathematical subject the last decade has seen a lot of work on this subject which is reviewed here we put an emphasis on mathematical aspects in particular the global existence question qualitative properties of solutions explicit solutions and the fluid dynamical limit the mechanical background is discussed more concisely in part i numerous contributions concerning other questions are outlined we try to give a complete reference list up to and including 1985

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

global existence of smooth solutions and convergence to barenblatt solutions for the physical vacuum free boundary problem of compressible euler equations with damping for the physical vacuum free boundary problem with the sound speed being c1 2 holder continuous near vacuum boundaries of the one dimensional compressible euler equations with damping the global existence of the smooth solution is proved which is shown to converge to the barenblatt self similar solution for the porous media equation with the same total mass when the initial datum is a small perturbation of the barenblatt solution the pointwise convergence with a rate of density the convergence rate of velocity in the supremum norm and the precise expanding rate of the physical vacuum boundaries are also given the proof is based on a construction of higher order weighted functionals with both space and time weights capturing the behavior of solutions both near vacuum states and in large time an introduction of a new ansatz higher order nonlinear energy estimates and elliptic estimates 2016 wiley periodicals inc

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

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

the pointwise estimates of solutions for euler equations with damping in multi dimensions we study the time asymptotic behavior of solutions for the isentropic euler equations with damping in multi dimensions the global existence and pointwise estimates of the solutions are obtained furthermore we obtain the optimal lp 1 p convergence rate of the solution when it is a perturbation of a constant state our approach is based on a detailed analysis of the green function of the linearized system and some energy estimates

truncated newton methods and the modeling of complex immersed elastic structures truncated newton minimization methods are combined with peskin s immersed boundary method to facilitate investigation of the dynamic interaction between a viscous incompressible fluid and immersed elastic objects of complex structure applications to aquatic animal locomotion and platelet aggregation during blood clotting are presented 1993 john wiley sons inc

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

weak factorizations of operators in the group von neumann algebras of certain amenable groups and applications let g be a compact group whose local weight b g has uncountable cofinality let h be an amenable locally compact group and a g h be the fourier algebra of g h we prove that the group von neumann algebra vn g h a g h has the weak uniform a g h factorization property of level b g as a corollary we show that a g h is strongly arens irregular and the topological centre of uc2 g h is equal to the fourier stieltjes algebra b g h

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

the 3d compressible euler equations with damping in a bounded domain abstract we proved global existence and uniqueness of classical solutions to the initial boundary value problem for the 3d damped compressible euler equations on bounded domain with slip boundary condition when the initial data is near its equilibrium time asymptotically the density is conjectured to satisfy the porous medium equation and the momentum obeys to the classical darcy s law based on energy estimate we showed that the classical solution converges to steady state exponentially fast in time we also proved that the same is true for the related initial boundary value problem of porous medium equation and thus justified the validity of darcy s law in large time