# Convergence of bounded solutions of nonlinear parabolic problems on a bounded interval

Thursday 7th November, 1400, MC113 (C26)

Dr Daniel Hauer

from

University of Sydney

will speak on

Convergence of bounded solutions of nonlinear parabolic problems on a bounded interval: the singular case

In this talk we prove that for every and for every continuous function  which is Lipschitz continuous in the second variable, uniformly with respect to the first one , each bounded solution of the one-dimensional heat equation

with homogeneous Dirichlet boundary conditions converges as to a stationary solution. The proof follows an idea of Matano which is based on a comparison principle. Thus, a key step is to prove a comparison principle on non-cylindrical open sets.