Elliptic Partial Differential Equations: Volume 2: Reaction-Diffusion Equations

✍ Scribed by Vitaly Volpert (auth.)

• Publisher: Birkhäuser Basel
• Year: 2014
• Tongue: English
• Leaves: 796
• Series: Monographs in Mathematics 104
• Edition: 1
• Category: Library

✦ Synopsis

If 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.

✦ Table of Contents

Front Matter....Pages i-xviii
Front Matter....Pages 1-1
Reaction-diffusion Processes, Models and Applications....Pages 3-78
Methods of Analysis....Pages 79-121
Reaction-diffusion Problems in Bounded Domains....Pages 123-200
Reaction-diffusion Problems on the Whole Axis....Pages 201-324
Front Matter....Pages 325-326
Monotone Systems....Pages 327-390
Reaction-diffusion Problems with Convection....Pages 391-451
Reaction-diffusion Systems with Different Transport Coefficients....Pages 453-490
Nonlinear Boundary Conditions....Pages 491-517
Front Matter....Pages 519-519
Nonlocal Reaction-diffusion Equations....Pages 521-626
Multi-scale Models in Biology....Pages 627-696
Back Matter....Pages 697-784

✦ Subjects

Partial Differential Equations