Spatial segregation limit of traveling wave solutions for a fully nonlinear strongly coupled competitive system

Abstract

The paper is concerned with a singular limit for the bistable traveling wave problem in a very large class of two-species fully nonlinear parabolic systems with competitive reaction terms. Assuming existence of traveling waves and enough compactness, we derive and characterize the limiting problem. The assumptions and results are discussed in detail. The free boundary problem obtained at the limit is specified for important applications.

Keywords

• lotka–volterra
• traveling wave
• bistability
• nonlinear diffusion
• nonlinear advection