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.