English

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

Analysis of PDEs 2020-03-18 v3 Mathematical Physics Classical Analysis and ODEs Functional Analysis math.MP

Abstract

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

Cite

@article{arxiv.1810.12006,
  title  = {Existence and uniqueness of dynamic evolutions for a one-dimensional debonding model with damping},
  author = {Filippo Riva and Lorenzo Nardini},
  journal= {arXiv preprint arXiv:1810.12006},
  year   = {2020}
}

Comments

36 pages, 5 figures