# A continuous dependence result for a dynamic debonding model in dimension one

## TL;DR

This paper proves that solutions to a one-dimensional dynamic debonding model depend continuously on initial and boundary data, ensuring stability and predictability of the model under data variations.

## Contribution

It establishes a continuous dependence result for a coupled wave and Griffith's criterion system in one dimension, which was previously unaddressed.

## Key findings

- Solutions converge under general data assumptions
- The model exhibits stability with respect to initial and boundary data
- Convergence holds in multiple natural topologies

## Abstract

In this paper we address the problem of continuous dependence on initial and boundary data for a one-dimensional debonding model describing a thin film peeled away from a substrate. The system underlying the process couples the weakly damped wave equation with a Griffith's criterion which rules the evolution of the debonded region. We show that under general convergence assumptions on the data the corresponding solutions converge to the limit one with respect to different natural topologies.