Acta mathematica scientia, Series B >
THRESHOLD RESULT FOR SEMILINEAR PARABOLIC EQUATIONS WITH INDEFINITE NON-HOMOGENEOUS TERM
Received date: 2011-03-07
Online published: 2012-11-20
Supported by
The project was supported by Natural Science Foundation of China (10971061), Hunan Provincial Innovation Foundation For Postgraduate (CX2010B209).
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).
XIE Jun-Hui , DAI Qiu-Yi , LIU Fang . THRESHOLD RESULT FOR SEMILINEAR PARABOLIC EQUATIONS WITH INDEFINITE NON-HOMOGENEOUS TERM[J]. Acta mathematica scientia, Series B, 2012 , 32(6) : 2302 -2314 . DOI: 10.1016/S0252-9602(12)60180-5
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