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.
Mots-clés : Wave equation in time-dependent domains, singularities, dynamic debonding, dynamic energy release rate, Griffith’s criterion, dynamic fracture, crack initiation, thin films
@article{COCV_2019__25__A80_0,
author = {Lazzaroni, Giuliano and Nardini, Lorenzo},
title = {On the 1d wave equation in time-dependent domains and the problem of debond initiation},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {25},
year = {2019},
doi = {10.1051/cocv/2019006},
zbl = {1437.35445},
mrnumber = {4040713},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2019006/}
}
TY - JOUR AU - Lazzaroni, Giuliano AU - Nardini, Lorenzo TI - On the 1d wave equation in time-dependent domains and the problem of debond initiation JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2019 VL - 25 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2019006/ DO - 10.1051/cocv/2019006 LA - en ID - COCV_2019__25__A80_0 ER -
%0 Journal Article %A Lazzaroni, Giuliano %A Nardini, Lorenzo %T On the 1d wave equation in time-dependent domains and the problem of debond initiation %J ESAIM: Control, Optimisation and Calculus of Variations %D 2019 %V 25 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2019006/ %R 10.1051/cocv/2019006 %G en %F COCV_2019__25__A80_0
Lazzaroni, Giuliano; Nardini, Lorenzo. On the 1d wave equation in time-dependent domains and the problem of debond initiation. ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 80. doi : 10.1051/cocv/2019006. http://www.numdam.org/articles/10.1051/cocv/2019006/
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