A Nonlinear Hyperbolic Volterra Equation in Viscoelasticity.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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A general model for the nonlinear motion of a one dimensional, finite, homogeneous, viscoelastic body is developed and analysed by an energy method. It is shown that under physically reasonable conditions the nonlinear boundary, initial value problem has a unique, smooth solution global in time, provided the given data are sufficiently small and smooth, moreover, the solution and its derivatives of first and second order decay to zero as t yields infinity. Various modifications and generalizations, including two and three dimensional problems, are also discussed.
- Numerical Mathematics