Blow-up of solutions to Nakao's problem via an iteration argument

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:275

Article

Chen, Wenhui¹  Reissig, Michael² 

[1] Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai 200240, Peoples R China

[2] Tech Univ Bergakad Freiberg, Fac Math & Comp Sci, Inst Appl Anal, D-09596 Freiberg, Germany

关键词: Semilinear hyperbolic system;    Wave equation;    Damped wave equation;    Blow-up;   

DOI  :  10.1016/j.jde.2020.11.009

来源: Elsevier

【 摘 要 】

In this paper, we consider blow-up behavior of weak solutions to a weakly coupled system for a semilinear damped wave equation and a semilinear wave equation in R' . This problem is part of the so-called Nakao's problem proposed by Professor Mitsuhiro Nakao (Kyushu university) for a critical relation between the exponents p and q of the power nonlinearities. By applying an iteration method for unbounded multipliers with a slicing procedure, we prove blow-up of weak solutions for Nakao's problem even for small data. We improve the blow-up result and upper bound estimates for lifespan comparing with the previous research, especially, in higher dimensional cases. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free