کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6417035 | 1338514 | 2016 | 24 صفحه PDF | دانلود رایگان |
In the present paper, we study a lifespan of solutions to the Cauchy problem for semilinear damped wave equations(DW){ât2uâÎu+âtu=f(u),(t,x)â[0,T(ε))ÃRn,u(0,x)=εu0(x),xâRn,âtu(0,x)=εu1(x),xâRn, where nâ¥1, f(u)=±|u|pâ1u or |u|p, pâ¥1, ε>0 is a small parameter, and (u0,u1) is a given initial data. The main purpose of this paper is to prove that if the nonlinear term is f(u)=|u|p and the nonlinear power is the Fujita critical exponent p=pF=1+2n, then the upper estimate to the lifespan is estimated byT(ε)â¤expâ¡(Cεâp) for all εâ(0,1] and suitable data (u0,u1), without any restriction on the spatial dimension. Our proof is based on a test-function method utilized by Zhang [35]. We also prove a sharp lower estimate of the lifespan T(ε) to (DW) in the critical case p=pF.
Journal: Journal of Differential Equations - Volume 261, Issue 3, 5 August 2016, Pages 1880-1903