Speed Selection of Traveling Waves of a Reaction–Diffusion–Advection Equation with High-Order Terms

In this paper, we investigate the speed selection mechanism of traveling wave solutions for a reaction–diffusion–advection equation with high-order terms in a cylindrical domain. The study focuses the problem under two cases for Neumann boundary condition and Dirichlet boundary condition. By using the upper and lower solutions method, general conditions for both linear and nonlinear selections are obtained. When the equation is expanded to higher dimensions, literature examining this particular topic is scarce. In light of this, new results have been obtained for both linear and nonlinear speed selections of the equation with high-order terms. For different power exponents m and n, specific sufficient conditions for linear and nonlinear selections with the minimal wave speed are derived by selecting suitable upper and lower solutions. The impact of the power exponents m and n on speed selection is analyzed.