Geodesic
On the wave equation on moving domains: regularity, energy balance and application to dynamic debonding
Giuliano Lazzaroni1 ; Riccardo Molinarolo1 ; Filippo Riva2 ; Francesco Solombrino3 orcid
1Università degli Studi di Firenze, Italy
2Università degli Studi di Pavia, Italy
3Università degli Studi di Napoli Federico II, Italy
Interfaces and free boundaries, Tome 25 (2023) no. 3, pp. 401-454

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DOI

We revisit some issues about existence and regularity for the wave equation in noncylindrical 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.
DOI : 10.4171/ifb/485
Classification : 35-XX, 74-XX
Mots-clés : Wave equation, moving domains, energy balance, dynamic debonding, thin films, dynamic energy release rate, Griffith’s criterion

Giuliano Lazzaroni  1   ; Riccardo Molinarolo  1   ; Filippo Riva  2   ; Francesco Solombrino  3

1 Università degli Studi di Firenze, Italy
2 Università degli Studi di Pavia, Italy
3 Università degli Studi di Napoli Federico II, Italy 
Giuliano Lazzaroni; Riccardo Molinarolo; Filippo Riva; Francesco Solombrino. On the wave equation on moving domains: regularity, energy balance and application to dynamic debonding. Interfaces and free boundaries, Tome 25 (2023) no. 3, pp. 401-454. doi: 10.4171/ifb/485
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     title = {On the wave equation on moving domains: regularity, energy balance and application to dynamic debonding},
     journal = {Interfaces and free boundaries},
     pages = {401--454},
     year = {2023},
     volume = {25},
     number = {3},
     doi = {10.4171/ifb/485},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/485/}
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