Nonlinear Stability of Rarefaction Waves for a Viscoelastic Material with Memory

DOI10.2307/2154646zbMath0804.35070OpenAlexW4247261292MaRDI QIDQ4292722

Harumi Hattori

Publication date: 18 May 1994

Full work available at URL: https://doi.org/10.2307/2154646

zbMATH Keywords

stability of rarefaction wavesviscoelastic material with memory

Mathematics Subject Classification ID

First-order nonlinear hyperbolic equations (35L60) Initial value problems for first-order hyperbolic systems (35L45) Dynamical problems in solid mechanics (74Hxx)

Cites Work

• The Riemann problem for the system \(u_ t+\sigma _ x=0\) and \((\sigma - f(u))_ t+(\sigma -\mu f(u))=0\)
• The Cauchy problem in one-dimensional nonlinear viscoelasticity
• Asymptotic stability of rarefraction waves for 2\(\times 2\) viscous hyperbolic conservation laws - the two-modes case
• A model Riemann problem for Volterra equations
• Hyperbolic conservation laws with relaxation
• Nonlinear waves for viscoelasticity with fading memory
• Asymptotic stability of rarefaction waves for 2\(\times 2\) viscous hyperbolic conservation laws
• Nonlinear stability of rarefaction waves for compressible Navier-Stokes equations
• Asymptotics toward the rarefaction waves of the solutions of a one-dimensional model system for compressible viscous gas
• Energy methods for nonlinear hyperbolic volterra integrodifferential equations
• On a Nonlinear Hyperbolic Volterra Equation
• An integro-differential equation with application in heat flow
• A model for one-dimensional, nonlinear viscoelasticity

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