Abstract
We study two systems of reaction diffusion equations with monostable or bistable type of nonlinearitiesand with free boundaries. These systems are used as multi-species competitive model.For two-species models, we prove the existence of traveling wave solutions, each of which consistsof two semi-waves intersecting at the free boundary.For three-species models, we also obtain some traveling wave solutions. In this case, however, everytraveling wave solution consists oftwo semi-waves and one compactly supported wave in between, each intersecting with its neighbors at the free boundaries.
Highlights
We study the following two systems:
One of our purpose in this paper is to study problem (1.6)
We point out that similar conclusions as in Theorems 1.1 and 1.2 remain true for the models including four or more species. For such a model, one can construct a traveling wave which consists of two semi-waves and several compactly supported waves in between, each intersecting with its neighbor at the free boundary
Summary
Reaction diffusion equation, traveling wave solution, competitive model, free boundary problem. Problem (1.1) arises in the study of traveling wave solutions of the following system of reaction diffusion equations: Chang and Chen [3] recently study the traveling wave solution of (1.6) (i.e. problem (1.1)) with logistic type of nonlinearities: f (u) = u(1 − u), g(v) = v(1 − v).
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