On Solutions of Diffusive Lotka-Volterra Systems
Date Issued
2011
Date
2011
Author(s)
Hung, Li-Chang
Abstract
In the present work, we study diffusive Lotka-Volterra systems of two-species and three-species. For competitive systems of two species, the tanh method is applied to construct exact traveling wave solutions. Based on the Fujita-type results, the method of shifted coexistence is developed to find blow-up solutions of cooperative systems of two species (with Xian Liao). For competitive-cooperative and competitive systems of three species, we employ the method of super- and subsolutions to establish the existence of traveling wave solutions. By using the generalized tanh method, it is shown that exact (with M. Mimura et al.) and semi-exact (with Yu-Sheng Chiou) traveling wave solutions exist for competitive systems of three species. In addition, nonexistence of traveling wave solutions to competitive systems of three species is also established by the maximum principle. Finally, we show solutions to competitive systems of three species can be constructed from the solutions of the heat equation. Further investigations include how to study diffusion-enhanced long-term coexistence, which is an interesting new phenomenon discovered by means of the solutions constructed from the heat equation.
Subjects
Traveling wave solutions
Exact solutions
Lotka-Volterra
Type
thesis
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