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

doi:10.1016/S0252-9602(17)30003-6

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (2): 301-315.doi: 10.1016/S0252-9602(17)30003-6

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

钟延生¹, 孙春友²

1. Department of Mathematics, Fujian Normal University, Fuzhou 350117, China;
2. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China

收稿日期:2015-01-22 修回日期:2016-09-02 出版日期:2017-04-25 发布日期:2017-04-25
通讯作者: Yansheng ZHONG,E-mail:zhyansheng08@163.com E-mail:zhyansheng08@163.com
作者简介:Yansheng ZHONG,E-mail:zhyansheng08@163.com;Chunyou SUN,E-mail:sunchy@lzu.edu.cn
基金资助:
Supported by NSFC Grant (11401100, 10601021), the foundation of Fujian Education Department (JB14021), and the innovation foundation of Fujian Normal University (IRTL1206).

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

Yansheng ZHONG¹, Chunyou SUN²

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).

摘要/Abstract

摘要：

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 L^q(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.

关键词: Uniform quasi-differentiability, semigroup, reaction-diffusion equation

Abstract:

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

钟延生, 孙春友. UNIFORM QUASI-DIFFERENTIABILITY OF SEMIGROUP TO NONLINEAR BEACTION-DIFFUSION EQUATIONS WITH SUPERCRITICAL EXPONENT[J]. 数学物理学报(英文版), 2017, 37(2): 301-315.

Yansheng ZHONG, Chunyou SUN. UNIFORM QUASI-DIFFERENTIABILITY OF SEMIGROUP TO NONLINEAR BEACTION-DIFFUSION EQUATIONS WITH SUPERCRITICAL EXPONENT[J]. Acta mathematica scientia,Series B, 2017, 37(2): 301-315.

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

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

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