DYNAMICS OF GLOBAL SOLUTIONS OF A SEMILINEAR PARABOLIC EQUATION

Abstract

The purpose of this talk is to review recent progress on the dynamics of global solutions of the Cauchy problem for a parabolic equation with power nonlinearity. It is shown that in some parameter range, the largetime behavior of solutions is determined by the spatial decay rate of initial data. It is shown that depending on initial data, the solution exhibits growup, convergence to steady states and self-similar solutions, non-convergence and quiasi-convergence. Moreover, given a specific decay rate of initial data, we can determine the rate of grow-up and convergence in an explicit way.