A mixed problem for the wave equation in a time dependent domain

1966 ◽  
Vol 22 (1) ◽  
pp. 24-36 ◽  
Author(s):  
Earl D. Rogak
Keyword(s):  
Wave Equation ◽  
Mixed Problem ◽  
Time Dependent ◽  
Time Dependent Domain ◽  
Dependent Domain

An Asymptotic Solution for the Wave Equation in a Time-Dependent Domain

SIAM Review ◽  
1981 ◽  
Vol 23 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Catherine Garcia R. ◽  
A. A. Minzoni
Keyword(s):  
Wave Equation ◽  
Asymptotic Solution ◽  
Time Dependent ◽  
Time Dependent Domain ◽  
Dependent Domain

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

2019 ◽  
Vol 25 ◽  
pp. 80 ◽  
Author(s):  
Giuliano Lazzaroni ◽  
Lorenzo Nardini
Keyword(s):  
Wave Equation ◽  
Existence Result ◽  
Energy Criterion ◽  
Time Dependent ◽  
Initial Time ◽  
One Dimensional ◽  
Coupled Problem ◽  
Time Dependent Domain ◽  
The One ◽  
Dependent Domain

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 part of the paper we prove existence for the wave equation when the evolution of the domain is given; in the second part of the paper, 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 in dynamic fracture.

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