The Cauchy problem in one-dimensional nonlinear viscoelasticity
type: Item
instance of: scholarly article
title: The Cauchy problem in one-dimensional nonlinear viscoelasticity
zbMATH Open document ID: 0535.35057
DOI: 10.1016/0022-0396(85)90147-0
published in: Journal of Differential Equations
publication date: 1985-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 74Hxx
Mathematics Subject Classification ID: 35L15
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 3849725
zbMATH Keywords: Cauchy problem
zbMATH Keywords: nonlinear viscoelasticity
zbMATH Keywords: classical solution
zbMATH Keywords: global existence
zbMATH Keywords: decay
zbMATH Keywords: energy estimates
zbMATH Keywords: Volterra operator
zbMATH Keywords: strongly positive definite kernel
zbMATH Keywords: resolvent kernel
zbMATH Keywords: Laplace transform
zbMATH Keywords: hyperbolic Volterra equation
zbMATH Keywords: unbounded viscoelastic bar
author: William J. Hrusa
author: John A. Nohel
MaRDI profile type: Publication
full work available at URL: 0022-0396(85)90147-0
OpenAlex ID: W1965608577
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description: scientific article; zbMATH DE number 3849725