Traveling Wave Solutions of Competitive Models with Free Boundaries

TL;DR

This paper investigates traveling wave solutions in multi-species reaction-diffusion models with free boundaries, demonstrating existence results for two- and three-species systems with monostable or bistable nonlinearities.

Contribution

It establishes the existence of complex traveling wave solutions involving semi-waves and compactly supported waves in multi-species models with free boundaries.

Findings

Existence of traveling wave solutions for two-species models with semi-waves intersecting at free boundaries.

Existence of multi-wave solutions for three-species models, including semi-waves and a compactly supported wave.

Characterization of wave structures in reaction-diffusion systems with free boundaries.

Abstract

We study two systems of reaction diffusion equations with monostable or bistable type of nonlinearity and with free boundaries. These systems are used as multi-species competitive model. For two-species models, we prove the existence of a traveling wave solution which consists of two semi-waves intersecting at the free boundary. For three-species models, we also prove the existence of a traveling wave solution which, however, consists of two semi-waves and one compactly supported wave in between, each intersecting with its neighbor at the free boundary.