UBC Mathematics Colloquium
KPP pulsating traveling fronts within large drift
Thurs., Sept. 17, 2009, 2:00pm, WMAX 216
PIMS/WMAX Postdoctoral Colloquium Abstract: This talk is based on
a joint work with St\'ephane Kirsch. Pulsating traveling fronts are
solutions of heterogeneous reaction-advection-diffusion equations
that model some population dynamics. Fixing a unitary direction
e, it is a well-known fact that for nonlinearities of KPP type
(after Kolmogorov, Petrovsky and Piskunov, f(u)=u(1-u) is a
typical homogeneous KPP nonlinearity), there exists a minimal speed c*
such that a pulsating traveling front with a speed c in the direction
of e exists if and only if c\geq c^*. In a periodic heterogeneous
framework we have the formula of Berestycki, Hamel and Nadirashvili
(2005) for the minimal speed of propagation. This formula involves
elliptic eigenvalue problems whose coefficients are expressed in terms
of the geometry of the domain, the direction of propagation, and the
coefficients of reaction, diffusion and advection of our equation. In
this talk, I will describe the asymptotic behaviors of the minimal
speed of propagation within either a large drift, a mixture of large
drift and small reaction, or a mixture of large drift and large
diffusion. These ``large drift limits'' are expressed as maxima of
certain variational quantities over the family of ``first integrals''
of the advection field. I will give more details about the limit
and a necessary and sufficient condition for which the limit is equal
to zero in the 2-d case.
Note for Attendees:
Tea and cookies will be served afterwards.