Blow-up for semilinear wave equations with the scale invariant damping and super-Fujita exponent

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:263

Article

Lai, Ning-An¹  Takamura, Hiroyuki²  Wakasa, Kyouhei³ 

[1] Lishui Univ, Dept Math, Lishui City 323000, Peoples R China

[2] Future Univ Hakodate, Fac Syst Informat Sci, Dept Complex & Intelligent Syst, 116-2 Kamedanakano Cho, Hakodate, Hokkaido 0418655, Japan

[3] Muroran Inst Technol, Math Sci Res Unit, Coll Liberal Arts, 27-1 Mizumoto Cho, Muroran, Hokkaido 0508585, Japan

关键词: Damped wave equation;    Semilinear;    Blow-up;   

DOI  :  10.1016/j.jde.2017.06.017

来源: Elsevier

【 摘 要 】

The blow-up for semilinear wave equations with the scale invariant damping has been well-studied for sub-Fujita exponent. However, for super-Fujita exponent, there is only one blow-up result which is obtained in 2014 by Wakasugi in the case of non-effective damping. In this paper we extend his result in two aspects by showing that: (I) the blow-up will happen for bigger exponent, which is closely related to the Strauss exponent, the critical number for non-damped semilinear wave equations; (II) such a blow-up result is established for a wider range of the constant than the known non-effective one in the damping term. (C) 2017 The Authors. Published by Elsevier Inc.

【 授权许可】

Free