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

Prof. Hiroshi Matano (University of Tokyo)

Propagating terrace in one-dimensional semilinear
diffusion equation

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

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