Development of Singularities in Nonlinear Viscoelasticity
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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This paper discusses the motion of nonlinear viscoelastic materials with fading memory in one space dimension. It concentrates on viscoelastic solids and briefly remark on similar results for fluids. After formulating the mathematical problems, the authors survey results for global existence of classical solutions to the initial value problem, provided the initial data are sufficiently small. They then discuss in some detail the development of singularities in initially smooth solutions for large data. Keywords nonlinear hyperbolic problems Volterra integrodifferential equations dissipation decay shocks viscoelastic fluids.