A Variational Principle for the Asymptotic Speed of Fronts of the Density Dependent Diffusion--Reaction Equation
Abstract
We show that the minimal speed for the existence of monotonic fronts of the equation
u
t
=(
u
m
)
xx
+f(u)
with
f(0)=f(1)=0
,
m>1
and
f>0
in
(0,1)
derives from a variational principle. The variational principle allows to calculate, in principle, the exact speed for arbitrary
f
. The case
m=1
when
f
′
(0)=0
is included as an extension of the results.