Comparison Theorems for Reaction-Diffusion Systems Defined in an Unbounded Domain.
Abstract
Comparison theorem techniques have played a central role in the study of scalar, nonlinear, parabolic differential equations. These techniques have proven less successful in the study of systems of equations for several reasons. Usually a very strong monotonicity condition must be imposed on the nonlinear terms of the equations. This severely restricts the applicability of the comparison theorems. Furthermore, there are technical difficulties associated with unbounded domains for systems of equations which are not present for scalar equations. In this report we demonstrate how these difficulties can be overcome for certain systems of reaction-diffusion equations. These systems have numerous applications including nerve conduction and mathematical ecology. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1982
- Accession Number
- ADA116186
Entities
People
- David Terman
Organizations
- University of Wisconsin–Madison