具有Neumann边界条件及临界Sobolev指数的半线性抛物方程整体解的渐近性及L^q-估计  

Asymptotic Behavior and L^p-Estimate of Global Solution of Semilinear Parabolic Equation with Critical Sobolev Exponent and Neumann Boundary Condition

作　　者：王培林[1] 谭忠[2] 

机构地区：[1]福建农林大学计算机与信息学院,福建福州350002 [2]厦门大学数学系,福建厦门361005

出　　处：《厦门大学学报（自然科学版）》2004年第1期17-20,共4页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(10171083);福建农林大学青年教师基金(2001 91)资助

摘　　要：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)).

关 键 词：NEUMANN边界条件 临界SOBOLEV指数 整体解 半线性抛物方程 渐近性 L^q-估计 

分 类 号：O175.26[理学—数学]