WIAS Preprint No. 3129, (2024)

Existence and weak-strong uniqueness for damage systems in viscoelasticity


Authors

  • Lasarzik, Robert
    ORCID: 0000-0002-1677-6925
  • Rocca, Elisabetta
    ORCID: 0000-0002-9930-907X
  • Rossi, Riccarda
    ORCID: 0000-0002-7808-0261

2020 Mathematics Subject Classification

  • 35D30 35D35 74G25 74A45

Keywords

  • Damage, viscoelasticity, global-in-time weak solutions, local-in-time strong solutions, time discretization, generalized solutions, weak-strong uniqueness

DOI

10.20347/WIAS.PREPRINT.3129

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, emphweak and emphstrong 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 emphweak-strong uniqueness statement is proved by means of a suitable relative energy inequality.

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