Energy method for multi-dimensional balance laws with non-local dissipation

DOI10.1016/j.matpur.2009.10.007zbMath1197.35050OpenAlexW2019924952MaRDI QIDQ981629

Changjiang Zhu, Klemens Fellner, Renjun Duan

Publication date: 1 July 2010

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2009.10.007

zbMATH Keywords

stabilityrate of convergencetime-periodic solutionsenergy dissipation ratehyperbolic-elliptic systemhydrodynamics of radiating gasesoptimal time-decay estimatessmooth planar waves

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Hyperbolic conservation laws (35L65) A priori estimates in context of PDEs (35B45)

Related Items (15)

$$L^\infty $$ L ∞ -Stability of Discontinuous Traveling Waves in a Radiating Gas Model ⋮ OPTIMAL DECAY RATES TO CONSERVATION LAWS WITH DIFFUSION-TYPE TERMS OF REGULARITY-GAIN AND REGULARITY-LOSS ⋮ Decay of a model system of radiating gas ⋮ Asymptotic behavior of rarefaction waves for a model system of a radiating gas ⋮ Asymptotic Stability of Solutions to a Hyperbolic-Elliptic Coupled System of Radiating Gas on the Half Line ⋮ Nonlocal Conservation Laws. A New Class of Monotonicity-Preserving Models ⋮ Large time behavior of solutions to a diffusion approximation radiation hydrodynamics model ⋮ Convergence rates to the planar stationary solution to a 2D model of the radiating gas on half space ⋮ Unnamed Item ⋮ Decay property of regularity-loss type for nonlinear hyperbolic-elliptic system in multi-dimensions ⋮ Asymptotic Stability of Rarefaction Wave for the Inflow Problem Governed by the One-Dimensional Radiative Euler Equations ⋮ The initial value problem for a multi-dimensional radiation hydrodynamics model with viscosity ⋮ Asymptotic stability of a composite wave of two viscous shock waves for the one-dimensional radiative Euler equations ⋮ Pointwise estimates of solutions to conservation laws with nonlocal dissipation-type terms ⋮ $L^\infty$-stability of Discontinuous Traveling Waves in a Hyperbolic-Elliptic Coupled System

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(L^1\)-stability of constants in a model for radiating gases
• Time-periodic solutions of the Boltzmann equation
• The nonrelativistic limit in radiation hydrodynamics. I: Weak entropy solutions for a model problem
• Decay rates to the planar rarefaction waves for a model system of the radiating gas in \(n\) dimensions
• Hyperbolic balance laws with a dissipative non local source
• The pointwise estimates of solutions for a model system of the radiating gas in multi-dimensions
• A combination of energy method and spectral analysis for study of equations of gas motion
• The regularized Chapman-Enskog expansion for scalar conservation laws
• Global well-posedness and relaxation limits of a model for radiating gas.
• On spae-time decay properties of solutions to hyperbolic-elliptic coupled systems
• Large-time behavior of solutions to hyperbolic-elliptic coupled systems
• Numerical approximation of entropy solutions for hyperbolic integro-differential equations
• Optimal \(L^{1}\) rate of decay to diffusion waves for the Hamer model of radiating gases
• Optimal decay estimates on the linearized Boltzmann equation with time dependent force and their applications
• Shock profiles for non-equilibrium radiating gases
• Initial value problem and relaxation limits of the hamer model for radiating gases in several space variables
• A singular limit for hyperbolic-elliptic coupled systems in radiation hydrodynamics
• ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO A MODEL SYSTEM OF RADIATING GAS WITH DISCONTINUOUS INITIAL DATA
• Critical Thresholds in a Convolution Model for Nonlinear Conservation Laws
• A NONLOCAL CONSERVATION LAW WITH NONLINEAR "RADIATION" INHOMOGENEITY
• ASYMPTOTIC DECAY TOWARD THE PLANAR RAREFACTION WAVES FOR A MODEL SYSTEM OF THE RADIATING GAS IN TWO DIMENSIONS
• Shock Waves for a Model System of the Radiating Gas
• CAUCHY PROBLEM FOR A MODEL SYSTEM OF THE RADIATING GAS: WEAK SOLUTIONS WITH A JUMP AND CLASSICAL SOLUTIONS
• L^p ENERGY METHOD FOR MULTI-DIMENSIONAL VISCOUS CONSERVATION LAWS AND APPLICATION TO THE STABILITY OF PLANAR WAVES
• STABILITY OF RAREFACTION WAVES FOR A MODEL SYSTEM OF A RADIATING GAS
• Viscous and inviscid stability of multidimensional planar shock fronts
• BV Estimates on Lax–Friedrichs' Scheme or a Model of Radiating Gas
• ASYMPTOTIC DECAY TOWARD THE PLANAR RAREFACTION WAVES OF SOLUTIONS FOR VISCOUS CONSERVATION LAWS IN SEVERAL SPACE DIMENSIONS
• Convergence rates toward the travelling waves for a model system of the radiating gas
• Shock waves for radiative hyperbolic-elliptic systems
• Hyperbolic Balance Laws with a Non Local Source
• THE BOLTZMANN EQUATION IN THE SPACE $L^2\cap L^\infty_\beta$: GLOBAL AND TIME-PERIODIC SOLUTIONS
• NON-LINEAR EFFECTS ON THE PROPAGATION OF SOUND WAVES IN A RADIATING GAS
• Asymptotic Stability of Planar Rarefaction Waves for Viscous Conservation Laws in Several Dimensions

This page was built for publication: Energy method for multi-dimensional balance laws with non-local dissipation