Acta mathematica scientia,Series B ›› 2012, Vol. 32 ›› Issue (6): 2302-2314.doi: 10.1016/S0252-9602(12)60180-5

• Articles • Previous Articles     Next Articles

THRESHOLD RESULT FOR SEMILINEAR PARABOLIC EQUATIONS WITH INDEFINITE NON-HOMOGENEOUS TERM

 XIE Jun-Hui, DAI Qiu-Yi, LIU Fang   

  1. Department of Mathematics, Hunan Normal University, Changsha 410081, China
  • Received:2011-03-07 Online:2012-11-20 Published:2012-11-20
  • Supported by:

    The project was supported by Natural Science Foundation of China (10971061), Hunan Provincial Innovation Foundation For Postgraduate (CX2010B209).

Abstract:

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).

Key words: parabolic equations, initial boundary value problem, global solution, thresh-old result, non-homogenous term

CLC Number: 

  • 35K61
Trendmd