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Existence of large-data global weak solutions to a model of a strain-limiting viscoelastic body

Bulicek, Miroslav, Patel, Victoria, Sengul, Yasemin and Suli, Endre 2021. Existence of large-data global weak solutions to a model of a strain-limiting viscoelastic body. Communications on Pure and Applied Analysis 20 (5) , pp. 1931-1960. 10.3934/cpaa.2021053

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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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Publisher: American Institute of Mathematical Sciences (AIMS)
ISSN: 1534-0392
Date of First Compliant Deposit: 3 November 2021
Date of Acceptance: 4 January 2021
Last Modified: 01 Jun 2022 22:13
URI: https://orca.cardiff.ac.uk/id/eprint/145139

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