数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (6): 2302-2314.doi: 10.1016/S0252-9602(12)60180-5
谢君辉|戴求亿|刘芳
XIE Jun-Hui, DAI Qiu-Yi, LIU Fang
摘要:
In this paper, we study the threshold result for the initial boundary value problem of non-homogeneous semilinear parabolic equations
{ut − Δu = g(u) + λf(x), (x, t) ∈Ω × (0, T),
u = 0, (x, t) ∈ ∂Ω × [0, T),
u(x, 0) = u0(x) ≥ 0, x ∈Ω (P)
By combining a priori estimate of global solution with property of stationary solution set of problem (P), we prove that the minimal stationary solution Uλ(x) of problem (P) is stable, whereas, any other stationary solution is an initial datum threshold for the existence and
nonexistence of global solution to problem (P).
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