Zhong, Yansheng; Sun, Chunyou Uniform quasi-differentiability of semigroup to nonlinear reaction-diffusion equations with supercritical exponent. (English) Zbl 1389.37046 Acta Math. Sci., Ser. B, Engl. Ed. 37, No. 2, 301-315 (2017). Summary: A new approach is established to show that the semigroup \({\left\{ {S\left( t \right)} \right\}_{t \geq 0}}\) generated by a reaction-diffusion equation with supercritical exponent is uniformly quasi-differentiable in \({L^q}\left( \Omega \right)\left( {2 \leq q < \infty} \right)\) 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. Cited in 2 Documents MSC: 37L05 General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations 37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems 35K57 Reaction-diffusion equations Keywords:uniform quasi-differentiability; semigroup; reaction-diffusion equation PDFBibTeX XMLCite \textit{Y. Zhong} and \textit{C. Sun}, Acta Math. Sci., Ser. B, Engl. Ed. 37, No. 2, 301--315 (2017; Zbl 1389.37046) Full Text: DOI