Existence and weak-strong uniqueness for damage systems in viscoelasticity

2024/08/31 by Lasarzik, Robert, Rocca, Elisabetta, Rossi, Riccarda
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.00528

Abstract

In this paper we investigate the existence of solutions and their weak-strong uniqueness property for a PDE system modelling damage in viscoelastic materials. In fact, we address two solution concepts, weak and strong solutions. For the former, we obtain a global-in-time existence result, but the highly nonlinear character of the system prevents us from proving their uniqueness. For the latter, we prove local-in-time existence. Then, we show that the strong solution, as long as it exists, is unique in the class of weak solutions. This weak-strong uniqueness statement is proved by means of a suitable relative energy inequality.

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