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**Singular limit of a Fisher equation
with degenerate diffusion**

**D. Hilhorst (Université de Paris-Sud, Orsay)**

with R. Kersner, E. Logak and M. Mimura

**2 November 1999,
Department of Mathematics, Hiroshima University**

The purpose of this study is to gain a better understanding
of some reaction-diffusion models for bacterial colonies;
such models often have the form of a noncooperative
reaction-diffusion system with nonlinear diffusion
and the main unknown functions are the density of
a bacteria and the concentration of some nutrient.

In this talk we consider a simpler model involving
a Fisher equation with degenerate diffusion, namely

together with a homogeneous Neumann boundary condition
and a suitable initial condition. We prove that,
as
tends to zero,
converges to a limiting function *u*
which is almost everywhere equal to zero or to one and
that the interface between the regions where *u*=0
and *u*=1 moves according to the law

*V*_{n} = *c*_{*},

where *c*_{*} is the minimum velocity of the
travelling waves of a related equation.

*Tohru Okuzono*

*1999-10-27*