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Archive for August, 2009

Galois Correspodence

Thursday, August 27th, 2009

28th August 2009, 1400 MC206

Mr. Emilio Ferrer

from

UNE

will speak on

Galois Correspodence

Galois correspondence began as a relationship between particular extensions of fields and groups of automorphisms of those fields which leave each element of the original field fixed.

We introduce the concepts and present the main theorem, providing concrete examples.

Free Boundary Problems Describing Ecological Models

Wednesday, August 19th, 2009

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.

Solving the ∂-bar Problem Using Hölder Estimates in Non-Smooth Domains (20 Years Later)

Sunday, August 16th, 2009

17th August 2009, 1510 MC206

Dr. Gerd Schmalz

from

UNE

will speak on

Solving the -Problem Using Hölder Estimates in Non-Smooth Domains (20 Years Later)

The -complex is the complex analogue of the de Rham complex in differential geometry. It gives information on the solvability of the -problem: the p.d.e.

u=ƒ

for a differential form u with ƒ a given differential form on a domain in a complex manifold. In one complex dimension this reduces to the inhomogeneous Cauchy-Riemann equation

∂u/∂z

In the 1950s Andreotti and Grauert proved that the solvability of the -problem depends on convexity properties of the domain. Stronger versions of these results, with estimates on the solutions, were proved in the 1970s using integral formulæ for domains with smooth boundaries. My doctoral thesis generalised this to domains with non-smooth boundaries.