Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy
From MaRDI portal
Publication:5434613
DOI10.1002/cpa.20195zbMath1152.35009arXiv0805.3614OpenAlexW2078087062WikidataQ57776965 ScholiaQ57776965MaRDI QIDQ5434613
Stefano Bianchini, Roberto Natalini, Bernard Hanouzet
Publication date: 7 January 2008
Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0805.3614
decay estimatesdissipative, hyperbolic systems of balance lawsGreen function for the linearized problem
Asymptotic behavior of solutions to PDEs (35B40) First-order nonlinear hyperbolic equations (35L60) Initial value problems for first-order hyperbolic systems (35L45)
Related Items
GREEN'S FUNCTION AND LARGE TIME BEHAVIOR OF THE NAVIER–STOKES–MAXWELL SYSTEM ⋮ Stringent error estimates for one-dimensional, space-dependent \(2\times 2\) relaxation systems ⋮ A class of uniformly dissipative symmetric hyperbolic-hyperbolic systems ⋮ Hyperbolic balance laws: modeling, analysis, and numerics. Abstracts from the workshop held February 28 -- March 6, 2021 (hybrid meeting) ⋮ Frequency-localization Duhamel principle and its application to the optimal decay of dissipative systems in low dimensions ⋮ Entropy principle and recent results in non-equilibrium theories ⋮ Partially dissipative one-dimensional hyperbolic systems in the critical regularity setting, and applications ⋮ Relativistic kinetic theory of polyatomic gases: classical limit of a new hierarchy of moments and qualitative analysis ⋮ Semilinear behavior for totally linearly degenerate hyperbolic systems with relaxation ⋮ RELAXATION OF FLUID SYSTEMS ⋮ Time asymptotic high order schemes for dissipative BGK hyperbolic systems ⋮ An entropy functional and explicit decay rates for a nonlinear partially dissipative hyperbolic system ⋮ Can constitutive relations be represented by non-local equations? ⋮ The frequency-localization technique and minimal decay-regularity for Euler-Maxwell equations ⋮ Uniform global existence and convergence of Euler-Maxwell systems with small parameters ⋮ Nonresonant bilinear forms for partially dissipative hyperbolic systems violating the Shizuta-Kawashima condition ⋮ Asymptotic-numerical solution of nonlinear systems of one-dimensional balance laws ⋮ Partially dissipative hyperbolic systems in the critical regularity setting: the multi-dimensional case ⋮ Very high-order asymptotic-preserving schemes for hyperbolic systems of conservation laws with parabolic degeneracy on unstructured meshes ⋮ \(L^{p}-L^{q}\) decay estimates for dissipative linear hyperbolic systems in 1D ⋮ Large time behavior of entropy solutions to some hyperbolic system with dissipative structure ⋮ Global classical solutions to a kind of quasilinear hyperbolic systems in several space variables ⋮ Exact representation of the asymptotic drift speed and diffusion matrix for a class of velocity-jump processes ⋮ Global classical solutions to partially dissipative hyperbolic systems violating the Kawashima condition ⋮ On hyperbolic-dissipative systems of composite type ⋮ Global existence and asymptotic stability of smooth solutions to a fluid dynamics model of biofilms in one space dimension ⋮ Stability of aerostatic equilibria in porous medium flows ⋮ The Hyperbolic-Parabolic Chemotaxis System for Vasculogenesis: Global Dynamics and Relaxation Limit Toward a Keller–Segel Model ⋮ Stability of non-constant equilibrium solutions for two-fluid Euler-Maxwell systems ⋮ The dissipative property of the first order \(2\times 2\) hyperbolic system with constant coefficients ⋮ A \(2 \times 2\) simple model in which the sub-shock exists when the shock velocity is slower than the maximum characteristic velocity ⋮ Trend to Equilibrium for a Delay Vlasov--Fokker--Planck Equation and Explicit Decay Estimates ⋮ Global existence and decay of small solutions for quasi-linear second-order uniformly dissipative hyperbolic-hyperbolic systems ⋮ Formation of singularities in solutions to nonlinear hyperbolic systems with general sources ⋮ Global existence for partially dissipative hyperbolic systems in the \(L^p\) framework, and relaxation limit ⋮ Relaxation approximation and asymptotic stability of stratified solutions to the IPM equation ⋮ Partially dissipative systems in the critical regularity setting, and strong relaxation limit ⋮ Global classical solutions for partially dissipative hyperbolic system of balance laws ⋮ Uniform Asymptotic and Convergence Estimates for the Jin--Xin Model Under the Diffusion Scaling ⋮ Green’s function and pointwise convergence for compressible Navier-Stokes equations ⋮ An efficient asymptotic-numerical method to solve nonlinear systems of one-dimensional balance laws ⋮ Global existence of small solutions to the Kerr-Debye model for the three-dimensional Cauchy problem ⋮ Convergence of a vector-BGK approximation for the incompressible Navier-Stokes equations ⋮ Stability of non-constant equilibrium solutions for Euler-Maxwell equations ⋮ Asymptotic limit and decay estimates for a class of dissipative linear hyperbolic systems in several dimensions ⋮ The optimal decay estimates on the framework of Besov spaces for generally dissipative systems ⋮ Analysis of non-isentropic compressible Euler equations with relaxation ⋮ On Cauchy problems of thermal non-equilibrium flows with small data ⋮ Sub-shock formation in shock structure of a binary mixture of polyatomic gases ⋮ Global existence and decay estimates for the solution of a nonlinear Bresse system ⋮ Late-time/stiff-relaxation asymptotic-preserving approximations of hyperbolic equations ⋮ Global solution to initial boundary value problem for gas dynamics in thermal nonequilibrium ⋮ Global classical solutions to partially dissipative quasilinear hyperbolic systems with one weakly linearly degenerate characteristic ⋮ Global existence and decay of solutions of the Cauchy problem in thermoelasticity with second sound ⋮ Decay rates and global existence for semilinear dissipative Timoshenko systems ⋮ Validity of the Chapman-Enskog expansion for a class of hyperbolic relaxation systems ⋮ Global existence and long-time behavior of smooth solutions of two-fluid Euler-Maxwell equations ⋮ On relaxation hyperbolic systems violating the Shizuta-Kawashima condition ⋮ Weakly nonlinear-dissipative approximations of hyperbolic-parabolic systems with entropy ⋮ Large time asymptotics for partially dissipative hyperbolic systems ⋮ Error Estimates for well-balanced and time-split schemes on a locally damped wave equation ⋮ CFL condition, Boltzmann's H-theorem, Onsager reciprocal relations and beyond ⋮ Asymptotic preserving scheme for the shallow water equations with source terms on unstructured meshes ⋮ Decay estimates for hyperbolic balance laws ⋮ Thermal non-equilibrium flows in three space dimensions ⋮ The boundary Riemann solver coming from the real vanishing viscosity approximation ⋮ Uniform global existence and parabolic limit for partially dissipative hyperbolic systems ⋮ Global solution of 3D irrotational flow for gas dynamics in thermal nonequilibrium ⋮ Approximate models for stochastic dynamic systems with velocities on the sphere and associated Fokker-Planck equations ⋮ Large time behavior of solutions for hyperbolic balance laws ⋮ Boundary controllability and asymptotic stabilization of a nonlocal traffic flow model ⋮ Numerical convergence rate for a diffusive limit of hyperbolic systems: $p$-system with damping ⋮ Exponential stability of distributed parameter systems governed by symmetric hyperbolic partial differential equations using Lyapunov's second method ⋮ On an initial boundary value problem for gas dynamics in thermal nonequilibrium ⋮ \(L^p - L^q - L^r\) estimates and minimal decay regularity for compressible Euler-Maxwell equations ⋮ An admissibility and asymptotic preserving scheme for systems of conservation laws with source term on 2D unstructured meshes with high-order MOOD reconstruction ⋮ Asymptotic preserving HLL schemes ⋮ RELAXATION APPROXIMATION OF THE KERR MODEL FOR THE THREE-DIMENSIONAL INITIAL-BOUNDARY VALUE PROBLEM ⋮ Global classical solution to partially dissipative quasilinear hyperbolic systems ⋮ GLOBAL SOLUTIONS AND DECAY PROPERTY WITH REGULARITY-LOSS FOR QUASI-LINEAR HYPERBOLIC SYSTEMS WITH DISSIPATION ⋮ Asymptotic behavior of 2D stably stratified fluids with a damping term in the velocity equation ⋮ Asymptotic stability in a second-order symmetric hyperbolic system modeling the relativistic dynamics of viscous heat-conductive fluids with diffusion ⋮ Strong convergence of a vector-BGK model to the incompressible Navier-Stokes equations via the relative entropy method ⋮ Characterization of the dissipative structure for the symmetric hyperbolic system with non-symmetric relaxation ⋮ Global classical solutions to partially dissipative quasilinear hyperbolic systems with weaker restrictions on wave interactions ⋮ Stability and instability in scalar balance laws: fronts and periodic waves ⋮ Periodic BV solutions of hyperbolic balance laws with dissipative source ⋮ Time-asymptotic stability for first-order symmetric hyperbolic systems of balance laws in dissipative compressible fluid dynamics ⋮ Thermodynamically consistent modeling for complex fluids and mathematical analysis ⋮ On global solutions in one-dimensional thermoelasticity with second sound in the half line ⋮ Asymptotic stability of equilibrium state to the mixed initial-boundary value problem for quasilinear hyperbolic systems ⋮ Hyperbolic balance laws with relaxation
Cites Work
