Existence and uniqueness of dynamic evolutions for a one-dimensional debonding model with damping

TL;DR

This paper studies a one-dimensional debonding model with damping, proving existence and uniqueness of solutions for the wave equation coupled with a growth criterion for the debonded region.

Contribution

It establishes the existence and uniqueness of solutions for a damped wave equation coupled with a debonding criterion, advancing understanding of dynamic debonding processes.

Findings

Unique solution for the wave equation with assigned debonding front

Existence and uniqueness for the coupled wave and Griffith's criterion

Mathematical validation of the model's well-posedness

Abstract

In this paper we analyse a one-dimensional debonding model for a thin film peeled from a substrate when viscosity is taken into account. It is described by the weakly damped wave equation whose domain, the debonded region, grows according to a Griffith's criterion. Firstly we prove that the equation admits a unique solution when the evolution of the debonding front is assigned. Finally we provide an existence and uniqueness result for the coupled problem given by the wave equation together with Griffith's criterion.