Viscous shock profile and singular limit for hyperbolic systems with Cattaneo's law

DOI10.3934/krm.2018032zbMath1421.35216OpenAlexW2797307551WikidataQ129955480 ScholiaQ129955480MaRDI QIDQ1715952

Shuichi Kawashima, Tohru Nakamura

Publication date: 29 January 2019

Published in: Kinetic and Related Models (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/krm.2018032

zbMATH Keywords

convergence rateweighted energy methodrelaxation limitinitial layerscalar viscous conservation lawsartificial heat flux term

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Shocks and singularities for hyperbolic equations (35L67) Stability in context of PDEs (35B35) Singular perturbations in context of PDEs (35B25) Hyperbolic conservation laws (35L65) Nonlinear constitutive equations for materials with memory (74D10) Traveling wave solutions (35C07)

Related Items (4)

Linear stability of viscous shock wave for 1-D compressible Navier-Stokes equations with Maxwell’s law ⋮ Decay of the compressible Navier-Stokes equations with hyperbolic heat conduction ⋮ Global existence for a semi-discrete scheme of some quasilinear hyperbolic balance laws ⋮ Nonlinear stability of rarefaction waves for a hyperbolic system with Cattaneo's law

Cites Work

• Unnamed Item
• Asymptotic stability of traveling wave solutions of systems for one-dimensional gas motion
• The Euler limit and initial layer of the nonlinear Boltzmann equation
• Relaxation limit and initial layer to hydrodynamic models for semiconductors
• On the stability of damped Timoshenko systems: Cattaneo versus Fourier law
• Nonlinear asymptotic stability of viscous shock profiles for conservation laws
• Fluid dynamical limit of the nonlinear Boltzmann equation to the level of the compressible Euler equation
• Asymptotic stability of traveling waves for scalar viscous conservation laws with non-convex nonlinearity
• Nonlinear stability of viscous shock profile for a non-convex system of viscoelasticity
• Compressible Navier–Stokes Equations with hyperbolic heat conduction
• On the stability of travelling wave solutions of a one-dimensional model system for compressible viscous gas
• Navier-stokes and boltzmann shock profiles for a model of gas dynamics
• Stability of shock profiles in viscoelasticity with non‐convex constitutive relations
• Thermoelasticity with second sound?exponential stability in linear and non-linear 1-d
• STABILITY OF SHOCK PROFILES FOR NONCONVEX SCALAR VISCOUS CONSERVATION LAWS

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