# A dynamic model for viscoelastic materials with prescribed growing cracks

## TL;DR

This paper develops a mathematical model for viscoelastic materials with growing cracks, proving existence and uniqueness of solutions and highlighting additional energy dissipation mechanisms during crack growth.

## Contribution

It introduces a dynamic model for viscoelastic materials with evolving cracks, including existence, uniqueness, and energy dissipation analysis.

## Key findings

- Existence of solutions for viscoelastic systems with cracks
- Uniqueness under stronger regularity conditions
- Additional dissipation due to crack growth

## Abstract

In this paper we prove the existence of solutions for a class of viscoelastic dynamic systems on time--dependent cracked domains, with possibly degenerate viscosity coefficients. Under stronger regularity assumptions we also show a uniqueness result. Finally, we exhibit an example where the energy--dissipation balance is not satisfied, showing there is an additional dissipation due to the crack growth.