The asymptotic form of shocks in relaxing media
type: Item
instance of: scholarly article
title: The asymptotic form of shocks in relaxing media
zbMATH Open document ID: 0662.73018
DOI: 10.1016/0165-2125(88)90028-5
author: Gary R. Nicklason
published in: Wave Motion
publication date: 1988-01-01T00:00:00Z
review text: The Laplace transform is used to analyze the asymptotic solutions \((\alpha \to \pm \infty)\) of a class of integrodifferential equations encountered in the study of nonlinear viscoelastic problems. It is found that the step-up behaviour from the smaller equilibrium value (\(\alpha\) \(\to -\infty)\) is exponential, while the approach to the larger value (\(\alpha\) \(\to \infty)\) is dependent on the form of the relaxation function being considered. A perturbation solution to one of the equations is also given. The form of the lowest-order solution shows how the oscillatory nature of some of the previously presented solutions arises.
Mathematics Subject Classification ID: 74M20
Mathematics Subject Classification ID: 74D05
Mathematics Subject Classification ID: 74D10
Mathematics Subject Classification ID: 45M05
Mathematics Subject Classification ID: 74S30
zbMATH DE Number: 4083098
zbMATH Keywords: oscillatory asymptotic solution
zbMATH Keywords: Laplace transform
zbMATH Keywords: asymptotic solutions
zbMATH Keywords: integrodifferential equations
zbMATH Keywords: nonlinear viscoelastic problems
zbMATH Keywords: step-up behaviour
zbMATH Keywords: perturbation solution
zbMATH Keywords: lowest-order solution
MaRDI profile type: Publication
full work available at URL: 0165-2125(88)90028-5
OpenAlex ID: W2029357371
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description: scientific article; zbMATH DE number 4083098