Reaction-Diffusion Equations.

Reaction-diffusion equations arise as mathematical models in a series of important applications, e.g. in models of superconducting liquids, flame propagation, chemical kinetics, biochemical reactions, predator-prey systems in ecology and so on. Both numerical and mathematical analysis of reaction-diffusion equations are currently very active fields of research. Obviously, we cannot study the subject at an advanced level in the present text, but we can get a general feeling of what these problems are about. Our aim is merely to present some simple models and to explore some of their properties using finite difference schemes and energy estimates. Further examples can be found in the exercises.1 [ABSTRACT FROM AUTHOR]