Finite time blowup of solutions to semilinear wave equation in an exterior domain

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:484

Article

Sobajima, Motohiro¹  Wakasa, Kyouhei² 

[1] Tokyo Univ Sci, Fac Sci & Technol, Dept Math, 2641 Yamazaki, Noda, Chiba 2788510, Japan

[2] Kushiro Coll, Natl Inst Technol, Dept Creat Engn, 2-32-1 Otanoshike Nishi, Kushiro, Hokkaido 0840916, Japan

关键词: Semilinear wave equations;    Blowup;    Upper bound of lifespan;    Exterior domain;   

DOI  :  10.1016/j.jmaa.2019.123667

来源: Elsevier

【 摘 要 】

We consider the initial-boundary value problem of semilinear wave equation with nonlinearity vertical bar u vertical bar(p) in exterior domain in R-N (N >= 3). Especially, the lifespan of - blowup solutions with small initial data are studied. The result gives upper bounds of lifespan which is essentially the same as the Cauchy problem in R-N. At least in the case N = 4, their estimates are sharp in view of the work by Zha-Zhou [21]. The idea of the proof is to use special solutions to linear wave equation with Dirichlet boundary condition which are constructed via an argument based on Wakasa-Yordanov [15]. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free