**SMS scnews item created by Daniel Daners at Fri 30 Mar 2012 1437**

Type: Seminar

Distribution: World

Expiry: 2 Apr 2012

**Calendar1: 2 Apr 2012 1400-1500**

**CalLoc1: Carslaw 707A**

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

### PDE Seminar

# Large Interaction Problems

### Dancer

E.N. Dancer

University of Sydney

Mon 2 April
2012 2-3pm, Carslaw Room 707A

## Abstract

We discuss the behaviour of the nonlinear parabolic boundary value
problem

$$\begin{array}{ccc}\hfill \frac{\partial u}{\partial t}& ={d}_{1}\Delta u+f\left(u\right)-kuv\hfill & \hfill \\ \hfill \frac{\partial v}{\partial t}& ={d}_{2}\Delta v+g\left(v\right)-kuv\hfill \end{array}$$

on a bounded domain $D$
with homogeneous Dirichlet boundary conditions on the boundary
$\partial D$.
We are also interested in the problem where the
$v$
in the last term of the first equation is replaced by
${v}^{2}$ (with a
corresponding change in the second equation ). We are mainly interested in the problem
where $k$ is
large. We are also interested in similar systems of three or more equations. The
first type of system occurs in population models while the second occurs in phase
separation models. We are interested in the limiting behaviour of the
stationary solutions and the behaviour of the dynamical system for large
$k$. This
is joint work with Kelei Wang and Zhitao Zhang.

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