摘要
讨论了非经典反应扩散方程u_t-△u_t-△u=f(u)+g(x)当非线性项满足临界指数增长时,该方程在强拓扑空间H^2(Ω)∩H_0~1(Ω)中的指数吸引子的存在性.特别的,通过证明指数吸引子的存在性,可知文献[7,12,14]中的强拓扑空间中的全局吸引子有有限的分形维数.
In this article,we study the existence of exponential attractors in the strong topology space H^2(Ω) n H_0~1(Ω) for the nonclassical Diffusion Equation u_t — △_ut- △_u = f(u) + g(x) with critical exponent.In particular,after proving the existence of exponential attractors,we know that the global attractor in the strong topology space in[7,12,14]with finiteness of fractal dimension.
出处
《应用泛函分析学报》
CSCD
2013年第3期285-290,共6页
Acta Analysis Functionalis Applicata
关键词
非经典扩散方程
指数吸引子
临界指数
nonclassical diffusion equation
exponential attractors
critical exponent
