On the wave equation on moving domains: regularity, energy balance and application to dynamic debonding

  title={On the wave equation on moving domains: regularity, energy balance and application to dynamic debonding},
  author={Giuliano Lazzaroni and Riccardo Molinarolo and Filippo Riva and Francesco Solombrino},
  journal={Interfaces and Free Boundaries},
. We revisit some issues about existence and regularity for the wave equation in noncylindrical domains. Using a method of diffeomorphisms, we show how, through increasing regularity assumptions, the existence of weak solutions, their improved regularity and an energy balance can be derived. As an application, we give a rigorous definition of dynamic energy release rate density for some problems of debonding, and we formulate a proper notion of solution for such problems. We discuss the… 



On the 1d wave equation in time-dependent domains and the problem of debond initiation

Motivated by a debonding model for a thin film peeled from a substrate, we analyse the one-dimensional wave equation, in a time-dependent domain which is degenerate at the initial time. In the first

Radial solutions for a dynamic debonding model in dimension two

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

In this paper we analyse a one-dimensional debonding model when viscosity is taken into account. It is described by the weakly damped wave equation whose domain, the debonded region, grows according

Dynamic fracture: an example of convergence towards a discontinuous quasistatic solution

Considering a one-dimensional problem of debonding of a thin film in the context of Griffith’s theory, we show that the dynamical solution converges, when the speed of loading goes down to 0, to a

A Continuous Dependence Result for a Dynamic Debonding Model in Dimension One

  • F. Riva
  • Mathematics
    Milan Journal of Mathematics
  • 2019
In this paper we address the problem of continuous dependence on initial and boundary data for a one-dimensional dynamic debonding model describing a thin film peeled away from a substrate. The

Energy-dissipation balance of a smooth moving crack

On the Approximation of Quasistatic Evolutions for the Debonding of a Thin Film via Vanishing Inertia and Viscosity

  • F. Riva
  • Mathematics
    J. Nonlinear Sci.
  • 2020
It is proved that, in contrast to what happens in the undamped case, dynamic solutions converge to the quasistatic one when inertia and viscosity go to zero, except for a possible discontinuity at the initial time.

Dynamics for the damped wave equations on time-dependent domains

We consider the asymptotic dynamics of a damped wave equations on a time-dependent domains with homogeneous Dirichlet boundary condition, the nonlinearity is allowed to have a cubic growth rate which

Variational Equations of Schroedinger-Type in Non-cylindrical Domains

Abstract Cauchy-Dirichlet problems are studied for linear Schroedinger-type partial differential equations in non–cylindrical domains by assuming a monotonicity condition on their sections with