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 latex-image-2 and for every continuous function latex-image-1 which is Lipschitz continuous in the second variable, uniformly with respect to the first one , each bounded solution of the one-dimensional heat equation
latex-image-2
with homogeneous Dirichlet boundary conditions converges as latex-image-1 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.