Uniqueness and continuous dependence for a viscoelastic problem with memory in domains with time dependent cracks

TL;DR

This paper investigates hyperbolic integro-differential systems in domains with evolving cracks, establishing conditions for solution uniqueness and stability relative to crack changes.

Contribution

It provides new criteria ensuring uniqueness and continuous dependence of solutions for viscoelastic problems with memory in dynamic cracked domains.

Findings

Conditions for solution uniqueness in cracked domains

Criteria for continuous dependence on crack evolution

Application to viscoelastic systems with memory

Abstract

We study some hyperbolic partial integro-differential systems in domains with time dependent cracks. In particular, we give conditions on the cracks which imply the uniqueness of the solution with prescribed initial-boundary conditions, and its continuous dependence on the cracks.