Monographs in Mathematics

Elliptic Partial Differential Equations

Volume 2: Reaction-Diffusion Equations

Authors: Volpert, Vitaly

  • Offers a systematic investigation of reaction-diffusion equations including existence, stability and bifurcations of solutions
  • Presents numerous examples and applications from population dynamics, chemical physics, biomedical models
  • Sequel to successful first volume
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  • ISBN 978-3-0348-0813-2
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  • Immediate eBook download after purchase
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price for USA
  • ISBN 978-3-0348-0812-5
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About this book

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.

About the authors

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.

Reviews

“This volume is concerned with the mathematical analysis of reaction-diffusion partial differential equations in relationship with their multiple applications. … This volume is useful to researchers in pure and applied nonlinear analysis and to graduate students in mathematics and mathematical physics.” (Vicenţiu D. Rădulescu, Mathematical Reviews, November, 2015)


Table of contents (10 chapters)

  • Reaction-diffusion Processes, Models and Applications

    Volpert, Vitaly

    Pages 3-78

  • Methods of Analysis

    Volpert, Vitaly

    Pages 79-121

  • Reaction-diffusion Problems in Bounded Domains

    Volpert, Vitaly

    Pages 123-200

  • Reaction-diffusion Problems on the Whole Axis

    Volpert, Vitaly

    Pages 201-324

  • Monotone Systems

    Volpert, Vitaly

    Pages 327-390

Buy this book

eBook $149.00
price for USA (gross)
  • ISBN 978-3-0348-0813-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $189.00
price for USA
  • ISBN 978-3-0348-0812-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Elliptic Partial Differential Equations
Book Subtitle
Volume 2: Reaction-Diffusion Equations
Authors
Series Title
Monographs in Mathematics
Series Volume
104
Copyright
2014
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
Distribution Rights
Distribution rights for India: Delhi Book Store, New Delhi, India
eBook ISBN
978-3-0348-0813-2
DOI
10.1007/978-3-0348-0813-2
Hardcover ISBN
978-3-0348-0812-5
Series ISSN
1017-0480
Edition Number
1
Number of Pages
XVIII, 784
Number of Illustrations and Tables
27 b/w illustrations, 17 illustrations in colour
Topics