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

Abstract

We revisit some issues about existence and regularity for the wave equation in noncylindrical domains. Using a method of diffeomorphisms we show, through increasing regularity assumptions, how 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 solutions for such problems. We compare the consistence of such a formulation with that of previous ones, given in the literature for particular cases.