On the wave equation on moving domains: regularity, energy balance and application to dynamic debonding

TL;DR

This paper investigates the wave equation on moving domains, establishing regularity and energy balance results, and applies these findings to define energy release rates in dynamic debonding problems.

Contribution

It introduces a method using diffeomorphisms to analyze existence, regularity, and energy balance for wave equations on noncylindrical domains, with applications to debonding.

Findings

Existence of weak solutions under regularity assumptions

Improved regularity results for solutions

A rigorous definition of dynamic energy release rate density

Abstract

We revisit some issues about existence and regularity for the wave equation in noncylindrical domains. Using a method of diffeomorphisms, we show how, through increasing regularity assumptions, the existence of weak solutions, their improved regularity and an energy balance can be derived. As an application, we give a rigorous definition of dynamic energy release rate density for some problems of debonding, and we formulate a proper notion of solution for such problems. We discuss the consistence of such formulation with previous ones, given in literature for particular cases.