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

# 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.

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