Oberseminar Mathematik in den Naturwissenschaften: Giuliano Lazzaroni, The wave equation on a time-dependent interval and the problem of dynamic debonding

Abstract:

Motivated by a debonding model for a thin film peeled from a substrate, we analyse the onedimensional wave equation, in a time-dependent domain which is possibly degenerate at the initial time. First we prove existence for the wave equation when the evolution of the domain is given; then, we consider the problem where 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 and evolution in dynamic fracture.