Nonlinear Diffusion–Reaction Phenomena

Abstract

Many physical phenomena are described by the interaction of convection and diffusion and also by the interaction of diffusion and reaction. From a physical point of view, the convection–diffusion process and the diffusion–reaction process are quite fundamental in describing a wide variety of problems in physical, chemical, biological, and engineering sciences. Some nonlinear partial differential equations that model these processes provide many new insights into the question of interaction of nonlinearity and diffusion. It is well known that the Burgers equation is a simple nonlinear model equation representing phenomena described by a balance between convection and diffusion. The Fisher equation is another simple nonlinear model equation which arises in a wide variety of problems involving diffusion and reaction.