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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:505

Article

Nakao, Mitsuhiro¹ 

[1] Kyushu Univ, Fac Math, Fukuoka 8190395, Japan

关键词: Wave equation;    Unique continuation;    Noncylindrical domain;    Initial boundary value problem;   

DOI  :  10.1016/j.jmaa.2021.125583

来源: Elsevier

【 摘 要 】

We prove a unique continuation property for the wave equation in a time-dependent domain Omega(t), 0 <= t <= T. That is, if u(t) is a finite energy solution of the equation utt -Delta u = 0, x is an element of Omega(t), with u(x, t)(partial derivative Omega(t)) = 0, 0 <= t <= T, satisfying u(t) = 0 on some neighborhood omega (t) of a portion of the boundary partial derivative Omega(t), 0 <= t <= T, then we have u(t) = 0 on 12(t), 0 <= t <= T, under the assumptions that T is sufficiently large and 12(t) does not move so rapidly. (c) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free