Motivated by a debonding model for a thin film peeled from a substrate, we analyse the one-dimensional wave equation, in a time-dependent domain which is degenerate at the initial time. In the first part of the paper we prove existence for the wave equation when the evolution of the domain is given; in the second part of the paper, the evolution of the domain is unknown and is governed by an energy criterion coupled with the wave equation. Our existence result for such coupled problem is a contribution to the study of crack initiation in dynamic fracture.
On the 1d wave equation in time-dependent domains and the problem of debond initiation / Lazzaroni, Giuliano; Nardini, Lorenzo. - In: ESAIM. COCV. - ISSN 1292-8119. - ELETTRONICO. - 25:(2019), pp. 0-0. [10.1051/cocv/2019006]
On the 1d wave equation in time-dependent domains and the problem of debond initiation
Lazzaroni, Giuliano
;
2019
Abstract
Motivated by a debonding model for a thin film peeled from a substrate, we analyse the one-dimensional wave equation, in a time-dependent domain which is degenerate at the initial time. In the first part of the paper we prove existence for the wave equation when the evolution of the domain is given; in the second part of the paper, the evolution of the domain is unknown and is governed by an energy criterion coupled with the wave equation. Our existence result for such coupled problem is a contribution to the study of crack initiation in dynamic fracture.
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