Calculus of Variations and Geometric Measure Theory

G. Lazzaroni - R. Molinarolo - F. Riva - F. Solombrino

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

created by lazzaroni on 09 Mar 2022
modified by riva on 13 Dec 2022


Published Paper

Inserted: 9 mar 2022
Last Updated: 13 dec 2022

Journal: Interfaces Free Bound.
Year: 2022
Doi: 10.4171/IFB/485

ArXiv: 2203.03738 PDF


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.

Keywords: wave equation, Thin films, Griffith's criterion, Dynamic debonding, Dynamic energy release rate, Moving domains, Energy balance