TY - JOUR
T1 - Damped wave equation with a critical nonlinearity in higher space dimensions
AU - Hayashi, Nakao
AU - Naumkin, Pavel I.
N1 - Funding Information:
The work of N.H. is partially supported by JSPS KAKENHI Grant Numbers JP25220702 , JP15H03630 . The work of P.I.N. is partially supported by CONACYT and PAPIIT project IN100113 .
Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2017/2/1
Y1 - 2017/2/1
N2 - We study the Cauchy problem for nonlinear damped wave equations with a critical defocusing power nonlinearity |u|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.
AB - We study the Cauchy problem for nonlinear damped wave equations with a critical defocusing power nonlinearity |u|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.
KW - Critical nonlinearity
KW - Damped wave equation
KW - Higher space dimension
KW - Large time asymptotics
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U2 - 10.1016/j.jmaa.2016.09.005
DO - 10.1016/j.jmaa.2016.09.005
M3 - Article
AN - SCOPUS:84994351480
SN - 0022-247X
VL - 446
SP - 801
EP - 822
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -