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

Abstract:

In this paper, we study the threshold result for the initial boundary value problem of non-homogeneous semilinear parabolic equations
{u_t − 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 U_λ(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