The Riemann problem for the system \(u_ t+\sigma _ x=0\) and \((\sigma - f(u))_ t+(\sigma -\mu f(u))=0\)

DOI10.1007/BF00251726zbMath0555.35083OpenAlexW1963884663MaRDI QIDQ760599

Ling Hsiao, James M. Greenberg

Publication date: 1983

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00251726

zbMATH Keywords

asymptotic behaviourshock wavepropagationtraveling wavejump discontinuitymotion of a viscoelastic solid

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Shocks and singularities for hyperbolic equations (35L67) First-order nonlinear hyperbolic equations (35L60)

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CAUCHY PROBLEM FOR A MODEL SYSTEM OF THE RADIATING GAS: WEAK SOLUTIONS WITH A JUMP AND CLASSICAL SOLUTIONS, Hyperbolic conservation laws with relaxation, Global existence of classical solutions for the gas flows near vacuum through ducts expanding with space and time, Global resolvability for a viscoelastic model with relaxation, Well-posedness of the global entropy solution to the Cauchy problem of a hyperbolic conservation laws with relaxation, Existence of global weak solutions for a viscoelastic model with relaxation, Nonlinear Stability of Rarefaction Waves for a Viscoelastic Material with Memory, ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO A MODEL SYSTEM OF RADIATING GAS WITH DISCONTINUOUS INITIAL DATA, Existence of the entropy solution for a viscoelastic model, Existence and uniqueness of the global admissible solution for a viscoelastic model with relaxation, ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO A MODEL SYSTEM OF RADIATING GAS WITH DISCONTINUOUS INITIAL DATA, BV solutions and relaxation limit for a model in viscoelasticity, A model Riemann problem for Volterra equations, A difference scheme for a stiff system of conservation laws

Cites Work

• A priori estimates for flows in dissipative materials
• The existence and qualitative properties of solutions of \((\partial u/\partial t) + {1 \over 2} (\partial/\partial x) [u^2 + \int\limits_0^t c(s) u^2(x,t-s)ds=0\)]
• Solutions in the large for nonlinear hyperbolic systems of equations
• Existence of steady waves for a class of nonlinear dissipative materials