Existence and Geometry of Global Attractor for Reaction-Diffusion Equation with Concave-Convex Nonlinearity

摘要

In this paper, we are concerned with the existence and geometry of global attractor for reactiondiffusion equation with concave-convex nonlinearity. We firstly prove the existence of symmetric global attractor A for the reaction-diffusion equation that considered, after that applying the ideas of |1], we show the Z2 index of global attractor can be bigger than any positive integer m, and then from the Mane projection theorem (see |2|), the fractal dimension of global attractor is infinite.