A model Riemann problem for Volterra equations

DOI10.1007/BF00251725zbMath0514.45004MaRDI QIDQ1051210

Richard C. MacCamy

Publication date: 1983

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

zbMATH Keywords

Riemann problemviscoelasticitybalance lawVolterra equationsheat flow in material with memoryhereditary evolution equations

Mathematics Subject Classification ID

Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Thermodynamics in solid mechanics (74A15) Boundary value problems in the complex plane (30E25) Singular nonlinear integral equations (45G05) Dynamical problems in solid mechanics (74Hxx)

Related Items

Asymptotic stability in nonlinear elastic materials with dissipation ⋮ Accurate numerical simulation of a conservation law with memory ⋮ Nonlinear Stability of Rarefaction Waves for a Viscoelastic Material with Memory ⋮ On the Local Regularity of Solutions in Linear Viscoelasticity of Several Space Dimensions ⋮ On the Long-time Behaviour of Solutions to a Conservation Law with Memory

Cites Work

• Unnamed Item
• The Riemann problem for the system \(u_ t+\sigma _ x=0\) and \((\sigma - f(u))_ t+(\sigma -\mu f(u))=0\)
• Instability of steady shearing flows in a non-linear viscoelastic fluid
• Existence and nonexistence in the large of solutions of quasilinear wave equations
• Global solutions for an extended class of hyperbolic systems of conservation laws
• The existence and qualitative properties of solutions of \((\partial u/\partial t) + {1 \over 2} (\partial/\partial x) [u^2 + \int\limits_0^t c(s) u^2(x,t-s)ds=0\)]
• An integro-differential equation with application in heat flow
• Development of Singularities of Solutions of Nonlinear Hyperbolic Partial Differential Equations
• Decay of solutions of systems of nonlinear hyperbolic conservation laws