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UNIFORM QUASI-DIFFERENTIABILITY OF SEMIGROUP TO NONLINEAR REACTION-DIFFUSION EQUATIONS WITH SUPERCRITICAL EXPONENT
【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 Lq（?）（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.
【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（?）（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；
【Key words】 Uniform quasi-differentiability； semigroup； reaction-diffusion equation；
【Key words】 Uniform quasi-differentiability； semigroup； reaction-diffusion equation；
【基金】 Supported by NSFC Grant(11401100,10601021);the foundation of Fujian Education Department(JB14021);the innovation foundation of Fujian Normal University(IRTL1206)
- 【文献出处】 Acta Mathematica Scientia(English Series) ,数学物理学报(英文版) , 编辑部邮箱 ,2017年02期
- 【分类号】O175
- 【被引频次】2
- 【下载频次】36