A 3-Component System of Competition and Diffusion.

Abstract

This report studies the existence of non-constant solutions of certain two-point boundary value problems for 3-component systems with a small parameter epsilon, under homogeneous Neumann conditions at the boundaries. This problem is related to the analysis of segregation patterns in population models of 3-competing and spatially dispersing species. It is shown that the reduced problem (epsilon = 0) has many non-constant solutions exhibiting spatial segregation. Only a few of these, however, can serve as valid lowest-order approximations to solutions of the original problem when epsilon is non-zero but small. A singular perturbation construction clarifies which are in this category. The results of numerical computations of solutions are also illustrated. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1983
Accession Number
ADA132860

Entities

People

  • Masayasu Mimura
  • Paul C. Fife

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Coefficients
  • Competition
  • Construction
  • Differential Equations
  • Diffusion
  • Diffusion Coefficient
  • Equations
  • Inequalities
  • Inhibitors
  • Intervals
  • Mathematics
  • Perturbations
  • Spatial Distribution
  • Steady State
  • United States

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Speech Processing/Speech Recognition.