巴拿赫空间中半群指数吸引子的存在性

Existence of Exponential Attractors for Semigroup in Banach Space

中文关键词:  动力系统  指数吸引子  分形维数  非紧性测度

英文关键词:dynamical system  exponential attractors  fractal dimension  measure of Non-compactness

中文摘要:

      利用$\omega$-极限紧方法,建立了巴拿赫空间中半群指数吸引子的存在性,并给出了在一致凸的巴拿赫空间中证明指数吸引子存在性的方法.作为对理论结果的应用,证明了反应扩散方程指数吸引子的存在性.

英文摘要:

      We construct an exponential attractor for semigroup in Banach space by using $\omega$-limit compactness method and provide a new method to prove the existence of an exponential attractor in uniformly convex Banach space. As a simple application, we prove the existence of an exponential attractor for reaction diffusion equations.