A variational property of critical speed to travelling waves in the presence of nonlinear diffusion

Let ff be a continuous function in [0,1][0,1] with f(0)=0=f(1)f(0)=0=f(1) and f>0f>0 on ]0,1[]0,1[. We show that, under additional mild conditions on ff, the minimal speed for travelling waves of equation(0.1)∂u∂t=∂∂x[|∂u∂x|p−2∂u∂x]+f(u), may be computed via a constrained minimum problem which in turn is related to the solution of a singular boundary value problem in the half line.