Special Session 117: Patterns and Attractors in Nonlinear Dynamics

Traveling waves in the reaction-diffusion equation with discontinuity
Junsik Bae
Kyungpook National University
Korea
Co-Author(s):    Wonhyung Choi, Yong-Jung Kim
Abstract:
We classify traveling waves and stationary solutions of a reaction-diffusion equation arising in population dynamics with Allee-type effects. The reaction term is given by a quadratic polynomial with a discontinuity at zero, which captures finite-time extinction for sub-threshold populations. This discontinuity induces a free boundary in the wave profile, a phenomenon that distinguishes the model from the classical logistic or Allen-Cahn equations. A complete scenario is presented that connects monostable and bistable traveling waves through the wave speed parameter. This is a joint work with Wonhyung Choi (Hankyong National Univ.) and Yong-Jung Kim (KAIST).