EXISTENCE OF LARGE-DATA GLOBAL WEAK SOLUTIONS TO A MODEL OF A STRAIN-LIMITING VISCOELASTIC BODY

Abstract

We prove the existence of a unique large-data global-in-time weak solution to a class of models of viscoelastic bodies exhibiting strain-limiting behaviour, where the constitutive equation, relating the linearised strain tensor to the Cauchy stress tensor, is assumed to be of the implicit form. For a class of models, the existence of weak solution is established.

Keywords

• Nonlinear viscoelasticity
• strain-limiting theory
• evolutionary problem
• global existence
• weak solution
• regularity