Nonautonomous semilinear parabolic equations on an infinite interval

Dr. Jason Morris

Department of Mathematics
University of Alabama at Birmingham

January 27, 2006
202 Madison Hall
3:30 PM (Coffee and Cookies at 3:00)

Abstract

A topological degree for Fredholm operators is used to prove the existence of solutions for nonautonomous semilinear parabolic PDEs. These solutions exist for all positive times, and are shown to have particular asymptotic properties. In this talk, I will review some ideas of the finite-dimensional (Brouwer) topological degree, to motivate the topological degree for Fredholm operators. I will then indicate the assumptions that are made on the PDE in order to meet the requirements of the degree argument. Finally, I will describe one class of problems that satisfies all of the assumptions.