2026/07/21 by Thomas Giletti, Hirofumi Izuhara, Harunori Monobe
Mathematics · #math.AP
This work is devoted to the study of traveling wave solutions of reaction-diffusion systems, where the diffusion rate of~v, the second component, depends on~u, the first component. Such systems arise in prey-predator models, where the predator~v is actively hunting its prey~u, or in epidemiological models where the disease induces erratic behavior, for example rabies. This results in a quasilinear coupling in the highest-order term of the equation for~v. From the theoretical point of view, we fully classify traveling wave solutions when the first component does not diffuse, in which case the problem can be reduced to a nonlinear scalar equation. The case where both components diffuse is investigated numerically.