Phragmen–lindelöf principle for weak subsolutions and cooperative reaction–diffusion systems

Abstract

One of the principal techniques for treating sustems of reaction–diffusion equations is based on a comparison method using sub and super–solutions. In practice this method is much more effective if non–smooth subsolutions are allowed. In this note we extend the analysis in [2,3] for cooperative systems and prove a comparison principle for a natural and rather general class of weak subsolutions satisfying a Phragmen–Lindelöf condition. An application is then given to a biological model in involving a pair of mutualists.

Keywords:

• Comparison principle, reaction–diffusion
• subsolution
• mutualism

Additional information

Notes on contributors

J. Smoller

V. Hutson