Damped wave equation with a critical nonlinearity in higher space dimensions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:446

Article

Hayashi, Nakao¹  Naumkin, Pavel I.² 

[1] Osaka Univ, Grad Sch Sci, Dept Math, Osaka 5600043, Japan

[2] UNAM, Inst Matemat, Campus Morelia,AP 61-3 Xangari, Morelia 58089, Michoacan, Mexico

关键词: Damped wave equation;    Critical nonlinearity;    Large time asymptotics;    Higher space dimension;   

DOI  :  10.1016/j.jmaa.2016.09.005

来源: Elsevier

【 摘 要 】

We study the Cauchy problem for nonlinear damped wave equations with a critical defocusing power nonlinearity vertical bar u vertical bar(2/n) u, where n denotes the space dimension. For n = 1,2,3, global in time existence of small solutions was shown in [4]. In this paper, we generalize the results to any spatial dimension via the method of decomposition of the equation into the high and low frequency components under the assumption that the initial data are small and decay rapidly at infinity. Furthermore we present a sharp time decay estimate of solutions with a logarithmic correction. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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