Convergence of bounded solutions of nonlinear parabolic problems on a bounded interval

November 4th, 2013 by bmclaugh

Thursday 7th November, 1400, MC113 (C26)

Dr Daniel Hauer

from

University of Sydney

will speak on

Convergence of bounded solutions of nonlinear parabolic problems on a bounded interval: the singular case

In this talk we prove that for every latex-image-2 and for every continuous function latex-image-1 which is Lipschitz continuous in the second variable, uniformly with respect to the first one , each bounded solution of the one-dimensional heat equation
latex-image-2
with homogeneous Dirichlet boundary conditions converges as latex-image-1 to a stationary solution. The proof follows an idea of Matano which is based on a comparison principle. Thus, a key step is to prove a comparison principle on non-cylindrical open sets.

On a free boundary problem for the curvature flow with driving force

November 4th, 2013 by bmclaugh

Thursday 7th November, 1300, MC113 (C26)

Professor Hiroshi Matano

from

University of Tokyo

will speak on

On a free boundary problem for the curvature flow with driving force

This talk is concerned with a free boundary problem associated with the curvature dependent motion of planar curves in the upper half plane whose two endpoints slide along the horizontal axis with prescribed fixed contact angles. The first main result is on the classification of solutions; every solution falls into one of the three categories, namely, area expanding, area bounded and area shrinking types. We then study in detail the asymptotic behavior of solutions in each category. Among other things we show that solutions are asymptotically self-similar both in the area expanding and the area shriknking cases, while solutions converge to either a stationary solution or a traveling wave in the area bounded case. Thus the renormalized curve converges to some profile in each of the three cases, but the proof of the convergence is totally different among the three cases.

This is joint work with Jong-Shenq Guo, Masahiko Shimojo and Chang-Hong Wu.

On Monge-Ampere type equations and near field optics

October 19th, 2013 by bmclaugh

Thursday 24th October, 1400, MC113 (C26)

Professor Neil Trudinger

will speak on

On Monge-Ampere type equations and near field optics

We report on a general theory of Monge-Ampere type partial differential equations which are given by prescribing the Jacobians of vector mappings of one jets. Such PDEs arise in near field geometric optics and we consider some examples together with the underlying convexity and ensuing regularity theories.

Summer Workshop announced!

October 8th, 2013 by bmclaugh

Hello everyone,

Reserve the dates 3rd-6th December for the Maths department at UNE will again run a workshop this summer. The theme is “Complex Analysis and Differential Geometry” and will be partially supported by the AMSI.

Please visit the workshop website.

More information will be posted when it is available.

Bubbling Solutions for Chern-Simons Model in a Torus

September 27th, 2013 by bmclaugh

27th September 2013, 1530 MC113

Associate Professor Shusen Yan

from

University of New England

will speak on

Bubbling Solutions for Chern-Simons Model in a Torus

In this talk, I will present some results on the existence of different types of bubbling solutions for Chern-Simons model in torus. I will also talk about the exact number of solutions for this problem. (This is joint work with C.-S. Lin in NTU.)

Prof. Jianfu Yang (Jiangxi Normal Univ., China): Nonlinear elliptic problems with the fractional Laplacian

August 3rd, 2012 by schmalz

Prof. Jianfu Yang (Jiangxi Normal Univ., China)
will give a talk on

“Nonlinear elliptic problems with the fractional Laplacian”

Time and venue:

August 7 (Tuesday) at 2:15pm, seminar room 113 (C26)

Abstract:

In this talk, we present some existence and regularity results for nonlinear elliptic problems with the fractional Laplacian.

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

February 20th, 2012 by schmalz

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

January 19th, 2012 by schmalz

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

September 29th, 2011 by schmalz

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

September 29th, 2011 by schmalz

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