\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

On a limiting system in the Lotka--Volterra competition with cross-diffusion

Abstract Related Papers Cited by
  • In this paper we investigate a limiting system that arises from the study of steady-states of the Lotka-Volterra competition model with cross-diffusion. The main purpose here is to understand all possible solutions to this limiting system, which consists of a nonlinear elliptic equation and an integral constraint. As far as existence and non-existence in one dimensional domain are concerned, our knowledge of the limiting system is nearly complete. We also consider the qualitative behavior of solutions to this limiting system as the remaining diffusion rate varies. Our basic approach is to convert the problem of solving the limiting system to a problem of solving its "representation" in a different parameter space. This is first done without the integral constraint, and then we use the integral constraint to find the "solution curve" in the new parameter space as the diffusion rate varies. This turns out to be a powerful method as it gives fairly precise information about the solutions.
    Mathematics Subject Classification: 35J55.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(241) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return