Remark on the blow-up of solutions for the semilinear wave equation with overdamping term

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:478

Article

Nishihara, Kenji¹ 

[1] Waseda Univ, Tokyo 1698050, Japan

关键词: Semilinear wave equation;    Overdamping;    Blow-up;    Comparison theorem;   

DOI  :  10.1016/j.jmaa.2019.05.037

来源: Elsevier

【 摘 要 】

We consider the Cauchy problem for the wave equation with overdamping and semilinear source terms: {u(tt)-Delta u + b(t)u(t) = N(u), (t, x) is an element of R+ x R-N (u,u(t))(0,x) = (u(0), u(1))(x), x is an element of R-N, (P with b(t) = b(0)(t + 1)(beta) b(0) > 0, beta <-1 and N(u) = vertical bar u vertical bar(p-1)(u) > 1. Ikeda and Wakasugi [8] have recently showed that, when IN(u)1 < CluIP for any p > 1, there is a global-in-time solution to (P) for suitable small data, and that, when N(u) = luIP, the local-in-time solution blows up within a finite time for suitable large data. To show the blow-up result, their method seems to be not applicable to our semilinear term. Our aim is to show the blow-up of solutions for suitable large data, by the method much different from theirs. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free