**SMS scnews item created by Daniel Daners at Thu 4 Apr 2013 1414**

Type: Seminar

Modified: Thu 4 Apr 2013 1415

Distribution: World

Expiry: 8 Apr 2013

**Calendar1: 8 Apr 2013 1400-1500**

**CalLoc1: AGR Carslaw 829**

Auth: daners@como.maths.usyd.edu.au

### PDE Seminar

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

### Hauer

Daniel Hauer

University of Sydney

8 April 2013 14:00-15:00, Carslaw Room 829 (AGR)

## Abstract

In this talk we outline that for every \(1<p\leq 2\) and for every
continuous function \(f\colon [0,1]\times\mathbb R\to\mathbb R\), which
is Lipschitz continuous in the second variable, uniformly with respect
to the first one, each bounded solution of the one-dimensional heat
equation
\[
u_{t}-\bigl(|u_{x}|^{p-2}u_{x}\bigr)_{x}+f(x,u)=0
\qquad\text{in}\quad (0,1)\times
(0,+\infty)
\]
with homogeneous Dirichlet boundary conditions converges as
\(t\to +\infty\) 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.

Check also the PDE
Seminar page. Enquiries to Florica
Cîrstea or Daniel Daners.