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)