Exponential separation and asymptotic symmetry of solutions of parabolic equations
by
Peter Polacik
University of Minnesota

Symmetry of positive solutions of PDEs is a topic with long history. Since the first results of Gidas, Ni and Nirenberg in the seventies, it has been reappearing in the literature as a problem under investigation as well as a tool of investigation. For elliptic equations, the problem has been satisfactorily treated on both bounded and unbounded domains. For parabolic equations, results on bounded domains have been available since mid-nineties. In this lecture, we present new results on asymptotic symmetry of positive solutions on R^N.

The exponential separation for linear parabolic equations is another old theme and the second topic of the lecture. We shall present a new existence theorem on unbounded domains and show how it helps in the symmetry problem.

Date received: May 20, 2003