Volpert V. Elliptic Partial Differential Equations: Volume 2: Reaction-Diffusion Equations

Springer, Basel, 2014. — 796 p. — (Monographs in Mathematics. Volume 104) — ISBN: 3034808127If we had to formulate in one sentence what this book is about, it might be "How partial differential equations can help to understand heat explosion, tumor growth or evolution of biological species".
These and many other applications are described by reaction-diffusion equations. The theory of reaction-diffusion equations appeared in the first half of the last century. In the present time, it is widely used in population dynamics, chemical physics, biomedical modelling. The purpose of this book is to present the mathematical theory of reaction-diffusion equations in the context of their numerous applications. We will go from the general mathematical theory to specific equations and then to their applications. Existence, stability and bifurcations of solutions will be studied for bounded domains and in the case of travelling waves. The classical theory of reaction-diffusion equations and new topics such as nonlocal equations and multi-scale models in biology will be considered.Introduction to the Theory of Reaction-diffusion Equations
Reaction-diffusion Processes, Models and Applications
Methods of Analysis
Reaction-diffusion Problems in Bounded Domains
Reaction-diffusion Problems on the Whole Axis
Reaction-diffusion Waves in Cylinders
Monotone Systems
Reaction-diffusion Problems with Convection
Reaction-diffusion Systems with Different Transport Coefficients
Nonlinear Boundary Conditions
Nonlocal and Multi-scale Models
Nonlocal Reaction-diffusion Equations
Multi-scale Models in Biology