Journal title
Communications in Pure and Applied Analysis
DOI
10.3934/cpaa.2021053
Issue
5
Volume
20
Last updated
2024-03-25T18:53:15.133+00:00
Page
1931-1960
Abstract
We prove the existence of a unique large-data global-in-time weak solution to a class of models of the form utt=div T+f for viscoelastic bodies exhibiting strain-limiting behaviour, where the constitutive equation, relating the linearised strain tensor ε(u) to the Cauchy stress tensor T, is assumed to be of the form ε(ut)+αε(u)=F(T), where we define F(T)=(1+|T|a)−1aT, for constant parameters α∈(0,∞) and a∈(0,∞), in any number d of space dimensions, with periodic boundary conditions. The Cauchy stress T is shown to belong to L1(Q)d×d over the space-time domain Q. In particular, in three space dimensions, if a∈(0,27), then in fact T∈L1+δ(Q)d×d for a δ>0, the value of which depends only on a.
Symplectic ID
1152078
Submitted to ORA
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Publication type
Journal Article
Publication date
22 Mar 2021