Elliptic Partial Differential Equations

Volume 2: Reaction-Diffusion Equations
2014
ISBN: 978-3-0348-0812-5
Verlag: Springer

Buch, Englisch, Band 104, 784 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 13177 g

Reihe: Monographs in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Volpert, Vitaly

Fachgebiete

• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
• Naturwissenschaften Chemie Physikalische Chemie

Inhaltsverzeichnis

I. Introduction to the theory of reaction-diffusion equations.- Chapter 1. Reaction-diffusion processes, models and applications.- Chapter 2. Methods of analysis.- Chapter 3. Reaction-diffusion problems in bounded domains.- Chapter 4. Reaction-diffusion problems on the whole axis.- II. Reaction-diffusion waves in cylinders.- Chapter 5. Monotone systems.- Chapter 6. Reaction-diffusion problems with convection.- Chapter 7. Reaction-diffusion systems with different diffusion coefficients.- Chapter 8. Nonlinear boundary conditions.- Chapter 9. Nonlocal reaction-diffusion equations.- Chapter 10. Multi-scale models in biology.- Bibliographical comments.- Concluding remarks.- Acknowledgements.- References.- Index.

Über Autor(innen)

Vitaly Volpert started his scientific career in Russia and continued it in the USA and in France. He works on partial differential equations and on mathematical modelling in chemical physics, biology and medicine. He is an author of more than 200 scientific publications including three monographs.