刊名:Journal of Mathematical Analysis and Applications
出版年:2017
出版时间:1 February 2017
年:2017
卷:446
期:1
页码:801-822
全文大小:401 K
文摘
We study the Cauchy problem for nonlinear damped wave equations with a critical defocusing power nonlinearity , 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.