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

## TL;DR

This paper investigates the existence and properties of monotone traveling wave solutions for a reaction-diffusion equation involving a $(p, q)$-Laplacian operator, providing estimates of critical speeds and numerical insights.

## Contribution

It introduces new existence results for monotone heteroclinic waves in $(p, q)$-Laplacian driven equations and analyzes the influence of parameters $p$ and $q$ on wave dynamics.

## Key findings

- Derived estimates for critical wave speeds.
- Analyzed the impact of $p$ and $q$ on wave behavior.
- Provided numerical simulations illustrating theoretical results.

## Abstract

We study the existence of monotone heteroclinic traveling waves for the $1$-dimensional reaction-diffusion equation $$ u_t = (| u_x |^{p-2} u_x + | u_x |^{q-2} u_x)_x + f(u), $$ where the non-homogeneous operator appearing on the right-hand side is known as $(p, q)$-Laplacian. Here we assume that $2 \leq q < p$ and $f$ is a nonlinearity of Fisher type, namely it is always positive out of its zeros. 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.