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

Journal article

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.

Authors: Bulíček, M; Patel, V; Şengül, Y; Suli, E

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: American Institute of Mathematical Sciences
• Journal: Communications in Pure and Applied Analysis
• Volume: 20
• Issue: 5
• Pages: 1931-1960
• Publication date: 2021-03-22
• Acceptance date: 2021-01-04
• DOI: 10.3934/cpaa.2021053
• EISSN: 1553-5258
• ISSN: 1534-0392
• Language: English
• Keywords: strain-limiting theory; nonlinear viscoelasticity; regulatity; evolutionary problem; FFR; global existence; weak solution