摘要
本文获得了如下的奇异半线性反应扩散方程初值问题u/t - (1/tσ)Δu =up+f(x) ,limt→ 0 +u(t,x) =0 ,t >0 ,x ∈Rnx ∈Rn广义解 (mildsolution)在L∞loe[(0 ,∞ ) ;L∞(Rn) ]中的存在性 .其中σ>0 ,0 <p<1,f(x)非负且 f(x)∈L∞(Rn) .
In L ∞ Ioc [(0, ∞); L ∞(R n)], we obtained the existence of solutions to initial value problem of simelinear reaction diffusion equations with singular coefficient as following u/t-(1/t σ)Δu=u p+f(x), lim t→0 +u(t, x)=0, t>0, x∈R n x∈R n where σ>0, 0<p<1, f(x) is nonnegative and f(x)∈L ∞(R n).
出处
《经济数学》
2000年第2期67-71,共5页
Journal of Quantitative Economics
关键词
奇异半线性反应扩散方程
初值问题
解
存在性
Singular semilinear reaction diffusion equation, initial value problem, mild solution, Lipschitz condition
