On the 1d wave equation in time-dependent domains and the problem of debond initiation

created by lazzaroni on 28 Nov 2017
modified on 04 Feb 2019

[BibTeX]

Accepted Paper

Inserted: 28 nov 2017
Last Updated: 4 feb 2019

Journal: ESAIM: COCV
Year: 2019
Notes:

doi: 10.1051$/$cocv$/$2019006

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.