The Cauchy Problem in One-Dimensional Nonlinear Viscoelasticity.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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The authors study the initial value problem for a nonlinear hyperbolic Volterra equation which models the motion of an unbounded viscoelastic bar. Under physically motivated assumptions, we establish the existence of a unique, globally defined, classical solution provided the initial data are sufficiently smooth and small. They also discuss boundedness and asymptotic behavior. Their analysis is based on energy estimates in conjunction with properties of strongly positive definite kernels. Author
- Theoretical Mathematics