Calculus of Variations and Geometric Measure Theory

G. Lazzaroni - R. Molinarolo - F. Solombrino

Radial solutions for a dynamic debonding model in dimension two

created by lazzaroni on 09 Dec 2020
modified on 25 Feb 2022


Published Paper

Inserted: 9 dec 2020
Last Updated: 25 feb 2022

Journal: Nonlinear Anal.
Volume: 219
Number: 112822
Year: 2022
Doi: 10.1016/

ArXiv: 2012.04993 PDF


In this paper we deal with a debonding model for a thin film in dimension two, where the wave equation on a time-dependent domain is coupled with a flow rule (Griffith's principle) for the evolution of the domain. We propose a general definition of energy release rate, which is central in the formulation of Griffith's criterion. Next, by means of an existence result, we show that such definition is well posed in the special case of radial solutions, which allows us to employ representation formulas typical of one-dimensional models.