Monotone wave fronts for $(p, q)$-Laplacian driven reaction-diffusion equations
Maurizio Garrione, Marta Strani · Discrete and Continuous Dynamical Systems - S · 2018
We study the existence of monotone heteroclinic traveling waves for the $-dimensional reaction-diffusion equation$u_t = (\vert u_x \vert^{p-2} u_x + \vert u_x \vert^{q-2} u_x)_x + f(u), \;\;\;\; t ∈ \mathbb{R}, \; x ∈ \mathbb{R}, $where the non-homogeneous operator appearing on the right-hand side is of $(p, q)$-Laplacian type. Here we assume that $2 ≤ q 0$ 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.