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

We revisit some issues about existence and regularity for the wave equation in non-cylindrical 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.

Automated summary

This article revisits the issues of existence and regularity for the wave equation in non-cylindrical domains. Using diffeomorphisms, the authors demonstrate how weak solutions can be derived by increasing regularity assumptions and improving their regularity, while maintaining an energy balance. They also provide a rigorous definition of dynamic energy release rate density for debonding problems and formulate a proper notion of solutions for such problems. The consistency of this formulation is compared with previous ones found in the literature.