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.