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. - (In corso di stampa), pp. 0-0. [10.4171/IFB/485]
On the wave equation on moving domains: regularity, energy balance and application to dynamic debonding
Lazzaroni, Giuliano;Molinarolo, Riccardo;
In corso di stampa
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.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.