Volume 25, 2019
|Number of page(s)||21|
|Published online||10 December 2019|
On the 1d wave equation in time-dependent domains and the problem of debond initiation*,**
Università degli studi di Firenze, Dipartimento di Matematica e Informatica “U. Dini”,
viale Morgagni 67/a,
2 SISSA, via Bonomea 265, 34136 Trieste, Italy.
*** Corresponding author: firstname.lastname@example.org
Accepted: 21 January 2019
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.
Mathematics Subject Classification: 35L05 / 35Q74 / 35R35 / 74H20 / 74K35
Key words: Wave equation in time-dependent domains / singularities / dynamic debonding / dynamic energy release rate / Griffith’s criterion / dynamic fracture / crack initiation / thin films
When this research was carried out, GL was affiliated to SISSA (supported by the European Research Council under the Grant No. 290888 “Quasistatic and Dynamic Evolution Problems in Plasticity and Fracture”), to the University of Vienna (supported by the Austrian Science Fund (FWF) project P27052), and later to the University of Naples Federico II.
© EDP Sciences, SMAI 2019
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