Monotone wave fronts for (p, q)-Laplacian driven reaction-diffusion equations

We study the existence of monotone heteroclinic traveling waves for the 1-dimensional reaction-diffusion equation ut = (|ux| p − 2 ux + |ux| q − 2 ux)x + f(u), t ∈ R, x ∈ R, where the non-homogeneous operator appearing on the right-hand side is of (p, q)-Laplacian type. Here we assume that 2 ≤ q < p and f is a nonlinearity of Fisher type on [0, 1], namely f(0) = 0 = f(1) and f > 0 on ]0, 1[ . We give an estimate of the critical speed and we comment on the roles of p and q in the dynamics, providing some numerical simulations.