Asymptotic Behavior and L~p-Estimate of Global Solution of Semilinear Parabolic Equation with Critical Sobolev Exponent and Neumann Boundary Condition
- 数学科学－已发表论文 
研究一类具有Neumann边界条件及临界Sobolev指数的半线性抛物方程的整体解的渐近性及Lq 估计.这里Ω是RN(N≥3)中的有界光滑区域并且p=2 -1=N+2N-2.In this paper,we are concerned with the asymptotic behavior and L~p-estimate of the global solution of one kind of parabolic equation with critical sobolev exponent and neumann boundary condition. Here Ω is a smooth bounded domain in R~N(N≥ 3), and p=2~*-1=N+2N-2.We prove that: (1)If u(x,t;u_0) is a global solution with u_0∈∑,then u∈L~q(Ω×(t_0,∞)) for any q(2≤ q<∞) and any t_0>0,and (‖u‖_(L~q(Ω×(t_0,∞))))≤c, where constant c depends only on N,q,t_0 and Ω.In paticular,u is a classical solution of (1) for all t≥t_0>0.(2)If u(x,t;u_0) is a global solution with u_0∈∑,and uniformly bounded in H~1 with respect to t,then,for any subsquence t_n→∞,there exists a stationary for w such that u(x,t_n;u_0)w in (H~1(Ω)).