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

@article{Lazzaroni2022OnTW,
  title={On the wave equation on moving domains: regularity, energy balance and application to dynamic debonding},
  author={Giuliano Lazzaroni and Riccardo Molinarolo and Filippo Riva and Francesco Solombrino},
  journal={Interfaces and Free Boundaries},
  year={2022}
}
. 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… 
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