Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (2): 301-315.doi: 10.1016/S0252-9602(17)30003-6

• Articles • Previous Articles     Next Articles

UNIFORM QUASI-DIFFERENTIABILITY OF SEMIGROUP TO NONLINEAR BEACTION-DIFFUSION EQUATIONS WITH SUPERCRITICAL EXPONENT

Yansheng ZHONG1, Chunyou SUN2   

  1. 1. Department of Mathematics, Fujian Normal University, Fuzhou 350117, China;
    2. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
  • Received:2015-01-22 Revised:2016-09-02 Online:2017-04-25 Published:2017-04-25
  • Contact: Yansheng ZHONG,E-mail:zhyansheng08@163.com E-mail:zhyansheng08@163.com
  • Supported by:

    Supported by NSFC Grant (11401100, 10601021), the foundation of Fujian Education Department (JB14021), and the innovation foundation of Fujian Normal University (IRTL1206).

Abstract:

A new approach is established to show that the semigroup {S (t)}t ≥ 0 generated by a reaction-diffusion equation with supercritical exponent is uniformly quasi-differentiable in Lq(Ω) (2 ≤ q < ∞) with respect to the initial value. As an application, this proves the upper-bound of fractal dimension for its global attractor in the corresponding space.

Key words: Uniform quasi-differentiability, semigroup, reaction-diffusion equation

Trendmd