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.

On the wave equation on moving domains: regularity, energy balance and application to dynamic debonding / Lazzaroni, Giuliano; Molinarolo, Riccardo; Riva, Filippo; Solombrino, Francesco. - In: INTERFACES AND FREE BOUNDARIES. - ISSN 1463-9963. - ELETTRONICO. - 25:(2023), pp. 401-454. [10.4171/IFB/485]

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

Lazzaroni, Giuliano;Molinarolo, Riccardo;
2023

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.
2023
25
401
454
Lazzaroni, Giuliano; Molinarolo, Riccardo; Riva, Filippo; Solombrino, Francesco
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1303172
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