Seminario del Departamento de
Ecuaciones Diferenciales y Análisis Numérico

Fecha : 4 de junio de 2019
Hora  : 12:45
Lugar : Seminario del Departamento (Fac. de Matemáticas, 3a. planta, módulo 34)

Hongyong Cui

(Huazhong University of Science and Technology, Wuhan (China).)

Resumen

In this talk we are concerned with the continuity in initial data of a classical reaction-diffusion equation with arbitrary p>2 order nonlinearity and in any space dimension N≥1. We shall show that, with the external forcing only in L^2, the weak solutions can be strong (L^2 , L^r ∩H^1_0)-continuous for any r≥2 (independent of the physical parameters of the system), i.e., can converge in the norm of any L^r ∩H^1_0 as the corresponding initial values converge in L^2. The main technique we employ is a decomposition method of the nonlinearity, splitting the nonlinearity into two, one providing nice properties which leads to the desired results and the other remaining controllable. Applying this to the global attractor we will obtain some new topological properties as well as a upper bound of the fractal dimension of the attractor in L^r ∩H^1_0 by that in L^2 . This is a joint work with Profs. Peter Kloeden and Wenqiang Zhao.