The Cauchy problem in one-dimensional nonlinear viscoelasticity
We study the initial 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. We also discuss boundedness and asymptotic behavior. Our analysis is based on energy estimates in conjunction with properties of strongly positive definite kernels.
scientific article; zbMATH DE number 3849725
scientific article