19th August 2009, 1510 MC206

**Professor Zhigui Lin**

** **

from

Yangzhou University, China

will speak on

Free Boundary Problems Describing Ecological Models

This talk is concerned with a system of semilinear parabolic equations with a free boundary, which arises in a mutualistic ecological model. The local existence and uniqueness of a classical solution are obtained by using the Schauder ﬁxed point theorem. The asymptotic behavior of the free boundary is studied. Our results show that the free boundary problem admits a global slow solution if the inter-speciﬁc competitions are strong, while if the inter-speciﬁc competitions are weak there exist a blowup solution and a global fast solution.