Existence and weak-strong uniqueness for damage systems in viscoelasticity
Analysis of PDEs
2024-09-04 v1
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.
Keywords
Cite
@article{arxiv.2409.00528,
title = {Existence and weak-strong uniqueness for damage systems in viscoelasticity},
author = {Robert Lasarzik and Elisabetta Rocca and Riccarda Rossi},
journal= {arXiv preprint arXiv:2409.00528},
year = {2024}
}