On the question of global existence for reaction-diffusion systems with mixed boundary conditions

Abstract

The question of global existence for solutions of reaction-diffusion systems presents fundamental difficulties in the case in which some components of the system satisfy Neumann boundary conditions while others satisfy nonhomogeneous Dirichlet boundary conditions. We discuss particular examples for which classical solutions are known to exist globally when all components satisfy the same type of boundary condition and yet either finite-time blowup occurs or else global existence is unknown when mixed boundary condition types are imposed on the system. Some positive results are presented concerning global existence in the presence of mixed boundary conditions if certain structure requirements are placed on the system, and these results are applied to some particular chemical reaction models.