Wavefront solutions for a class of nonlinear highly degenerate parabolic equations

We consider the following nonlinear parabolic equation (F(v))x+(G(v))τ=(D(v))xx+ρ(v),v∈[α,β] where F, G are generic C1-functions in [α,β], D∈C1[α,β]∩C2(α,β) is positive inside (α,β) (possibly vanishing at the extreme points), and finally ρ is a monostable reaction term. We investigate the existence and the properties of travelling wave solutions for such an equation and provide their classification between classical and sharp solutions, together with an estimate of the minimal wave speed.