Traveling waves in nonclassical diffusion equations
Analysis of PDEs
2025-10-28 v1
Abstract
We study the existence of monotone traveling wave solutions in a class of nonclassical diffusion equations that include both standard diffusion and a higher-order mixed space-time dispersive term. The reaction term is nonlinear and subject to general structural conditions. By employing the method of upper and lower solutions, using less smooth super and subsolutions, we construct a monotone iterative scheme within a convex set and prove its convergence using Schauder's fixed point theorem. Explicit constructions of super and subsolutions are provided.
Cite
@article{arxiv.2510.22349,
title = {Traveling waves in nonclassical diffusion equations},
author = {William Barker and Le Xuan Dong and Vu Trong Luong and Nguyen Duong Toan},
journal= {arXiv preprint arXiv:2510.22349},
year = {2025}
}