Calculus of Variations and Geometric Measure Theory

F. Riva

A continuous dependence result for a dynamic debonding model in dimension one

created by riva on 04 Mar 2019
modified on 20 Nov 2019


Published Paper

Inserted: 4 mar 2019
Last Updated: 20 nov 2019

Journal: Milan Journal of Mathematics
Volume: 87
Number: 2
Pages: 315-350
Year: 2019
Doi: 10.1007/s00032-019-00303-5

ArXiv: 1903.01251 PDF
Links: Online version


In this paper we address the problem of continuous dependence on initial and boundary data for a one-dimensional debonding model describing a thin film peeled away from a substrate. The system underlying the process couples the weakly damped wave equation with a Griffith's criterion which rules the evolution of the debonded region. We show that under general convergence assumptions on the data the corresponding solutions converge to the limit one with respect to different natural topologies.

Keywords: Thin films, Griffith's criterion, Dynamic debonding, Wave equation in time-dependent domains, Continuous dependence