Terrace Solutions for Non-Lipschitz Multistable Nonlinearities

Traveling wave solutions of reaction-diffusion equations are well studied for Lipschitz continuous monostable and bistable reaction functions. These special play a key role in mathematical biology particular the study ecological invasions. However, if there more than two stable steady states, invasion phenomenon may become intricate involve intermediate steps, which leads one to consider not single but collection traveling waves with ordered speeds. In this paper we show that, function is discontinuous at then such exists even provides solution call terrace solution. More precisely, will address both existence uniqueness