摘要
本文考虑具有非线性边界条件-u_x(0,t)=u^q(0,t)在(0,T)半线性热方程u_t-u_(xx)=u^p在(0,∞)×(0,T)的正解.在初值的一些单调性假定下证明了c(T-t)^(-t)≤supu(x,t)≤C(T-0)^(-r)其中r=1/(p-1)如户>2q-1且r=1/[2(q-1)]如p≤2q-1.
This paper deals with positive solutions to semilinear heat equation u_t=u_(xx)+u^qin(0,∞)×(0.T)with the nonlinear boundary condition -u_x (0,t)=u^q(0,t) on (0,T). We prove that c(T-t)^(-r)≤supu(x,t)≤C(T-t)~r under some monotonicity assumptions on the initial value, where γ=1/(p-1) if q>2q-1 and γ=1/[2(q-)] if p≤2q-1.
出处
《应用数学》
CSCD
1998年第1期96-100,共5页
Mathematica Applicata
关键词
半线性热方程
非线性边界条件
爆破速度
Semilinear heat equation, Nonlinear boundary conditions,Blow-up rate