Yoshio Yamada of Waseda Univ (Japan) : Population models with nonlinear diffusion

Professor Yoshio Yamada of Waseda Univ (Japan) will give a talk at
Tuesday 3.10pm in MC206.

Title: Population models with nonlinear diffusion.

Abstract:
We will discuss Lotka-volterra competition models with nonlinear
diffusion. Under some conditions, these models exhibit segregation
phenomena between two competing species due to cross-diffusion effects.
We will give some recent results on global solutions for the
nonstationary problems and the structure of positive solutions for the
stationary problems.

Al Boggess (Texas A&M): Fundamental solutions to \Box_b on certain quadrics

Speaker: Al Boggess (Texas A&M)

Title: Fundamental solutions to \Box_b on certain quadrics

Time and venue: 17/01/2012, 2pm, Seminar room 206

Abstract: (joint work with Andy Raich)
In this talk, I will describe a process which can be used
to find the fundamental solution to \Box_b on quadric
submanifolds of complex Euclidean space. The tools will
involve representation theory using the Lie group structure
of quadrics along with Hermite expansions. In certain cases,
this leads to rather simple formulas for the fundamental solution.
In particular, we can provide formulas for the fundamental solution
for quadric hypersurfaces that are different than the Heisenberg
group and for the canonical quadric examples of codimension
two in C^4.

Hiroshi Matano (University of Tokyo): Propagating terrace in one-dimensional semilinear diffusion equation

Speaker:
Prof. Hiroshi Matano (University of Tokyo)

Title:
Propagating terrace in one-dimensional semilinear
diffusion equation

Abstract:
In this talk, I will discuss the asymptotic behavior of
solutions of one-dimensional semilinear diffusion
equation of the form
u_t = u_{xx} + f(x,u)
on the whole line, where f is a smooth function satisfying
f(x,0) = 0, f(x,u) = f(x+L,u) for some L > 0.

We consider the behavior of general solutions whose
intial data are either of the Heaviside function type or
compactly supported.

Under rather a mild additional assumption on f, we
show that the solution approaches, as t tends to infinity,
what we call a “propagating terrace”, which roughly means
a layer of pulsating traveling waves with different speeds.

In the special case where the nonlinearity f is monostable,
bistable or of the combustion type, the propagating terrace
is nothing but a single pulsating traveling front.
Our results answers many open questions concerning
the spreading fronts in periodic environments.

This is joint work with Thomas Giletti and Arnaud Ducrot.

Time and Venue:
2:10pm Tuesday Oct. 4, UNE Access Grid Room (IT building)

Vladimir Ejov (UniSA): Concept of `importance’ in hierarchical sporting competitions

Vladimir Ejov (UniSA) will give a talk on

“Concept of `importance’ in hierarchical sporting competitions”

Abstract. The scoring system for tennis comprises a hierarchical
structure where points combine to games, games combine to sets and
sets combine to form the match. Assuming that one side has a limited
supply of a resource which can improve performance at the lowest level
of hierarchy, we address the question how best to apply the limited
resource in order to optimise the probability of winning. Contests are
modelled probabilistically using binary trees and the concept of
`importance’ emerges as a key determinant of where to apply resources
optimally.

Tuesday, 27 September 2011, 3pm, C26: Seminar room 206

Exponential separation between positive and sign-changing solutions and its application in studies of threshold solutions of nonlinear parabolic equations

Mathematics Seminar

Speaker:
Prof. Peter Polacik, Univ of Minnesota

Time and Venue:
2:10pm, Tuesday (31 May, 2011), Access Grid Room in the ITD

Title:
Exponential separation between positive and sign-changing solutions and its
application in studies of threshold solutions of nonlinear parabolic
equations

Abstract:
In linear nonautonomous second-order parabolic equations, the exponential
separation refers to the exponential decay of  any sign-changing solution
relative to any positive solution. In time-autonoumous parabolic problems,
this property is closely related to properties of the principal eigenvalue
and eigenfunction of the corresponding elliptic operator.

In this lecture, after summarizing key results on  exponential separation,
we shall  show how it can be effectively used in studies of nonlinear
parabolic problems. In particular, we shall discuss sharp transitions from
extinction to propagation (or blowup) for a class of semilinear parabolic
equations on R^N.

System of Elliptic Equations

At 2pm on Tuesday, 24th May, 2011

Prof. Daomin Cao

from the Chinese Academy of Science

will speak in MC206 (Building C26)

on a

System of Elliptic Equations.

Abstract:

In this talk the speaker will consider a system of elliptic equations arising from physics. Previous results on the existence of solutions will be presented. The speaker
will also introduce the results on the existence of ground state in his joint work with I.L.Chern and J.C.Wei.

BOUNDARY BLOW UP ELLIPTIC PROBLEMS WITH SIGN-CHANGING WEIGHTS: EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS

On Tuesday, 17th May, 2011

JORGE GARCIA-MELIAN
Universidad de La Laguna

will speak on

BOUNDARY BLOW UP ELLIPTIC PROBLEMS WITH SIGN-CHANGING WEIGHTS: EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS

at 2pm in MC206.

Abstract. We consider an elliptic boundary blow-up problem in a bounded smooth domain of R^N, and show that as a parameter in the equation varies, the solution set form a smooth curve in a suitable function space, and the curve has a turning point at a critical value of the parameter. The proofs are mainly based on continuation methods.