Calculus of Variations and Geometric Measure Theory

F. Riva - L. Nardini

Existence and uniqueness of dynamic evolutions for a one-dimensional debonding model with damping

created by riva on 16 Jul 2018
modified on 01 Apr 2021


Published Paper

Inserted: 16 jul 2018
Last Updated: 1 apr 2021

Journal: Journal of Evolution Equations
Volume: 21
Number: 1
Pages: 63-106
Year: 2020
Doi: 10.1007/s00028-020-00571-4

ArXiv: 1810.12006v3 PDF
Links: Online version


In this paper we analyse a one-dimensional debonding model for a thin film peeled from a substrate when viscosity is taken into account. It is described by the weakly damped wave equation whose domain, the debonded region, grows according to a Griffith's criterion. Firstly we prove that the equation admits a unique solution when the evolution of the debonding front is assigned. Finally we provide an existence and uniqueness result for the coupled problem given by the wave equation together with Griffith's criterion.

Keywords: Griffith's criterion, Dynamic debonding, Wave equation in time-dependent domains, Dynamic energy release rate, Energy-dissipation balance, Maximum dissipation principle, Duhamel's principle