scholarly journals A unique continuation property for the wave equation in a time -dependent domain

2021 ◽  
pp. 125583
Author(s):  
Mitsuhiro Nakao
Keyword(s):  
Wave Equation ◽  
Unique Continuation ◽  
Time Dependent ◽  
Time Dependent Domain ◽  
Unique Continuation Property ◽  
Continuation Property ◽  
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.

scholarly journals Strict monotonicity and unique continuation of the biharmonic operator - doi: 10.5269/bspm.v30i2.14502

1970 ◽  
Vol 30 (2) ◽  
pp. 79-83
Author(s):  
Najib Tsouli ◽  
Omar Chakrone ◽  
Mostafa Rahmani ◽  
Omar Darhouche
Keyword(s):  
Unique Continuation ◽  
Biharmonic Operator ◽  
Strict Monotonicity ◽  
Unique Continuation Property ◽  
Continuation Property

In this paper, we will show that the strict monotonicity of the eigenvalues of the biharmonic operator holds if and only if some unique continuation property is satisfied by the corresponding eigenfunctions.

scholarly journals Unique continuation for non-negative solutions of quasilinear elliptic equations

2001 ◽  
Vol 64 (1) ◽  
pp. 149-156 ◽  
Author(s):  
Pietro Zamboni
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equation ◽  
Unique Continuation ◽  
Quasilinear Elliptic Equations ◽  
Kato Class ◽  
Unique Continuation Property ◽  
Continuation Property ◽  
Quasilinear Elliptic

Dedicated to Filippo ChiarenzaThe aim of this note is to prove the unique continuation property for non-negative solutions of the quasilinear elliptic equation We allow the coefficients to belong to a generalized Kato class.

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