Lecture Notes in Mathematics

Nonlinear Reaction-Diffusion Systems

Conditional Symmetry, Exact Solutions and their Applications in Biology

Authors: Cherniha, Roman, Davydovych, Vasyl'

  • Presents important results in solving nonlinear reaction-diffusion equations
  • Chapters contain ideas for further theoretical generalizations and examples for real world applications
  • Includes applications to pattern formation, ecology and population dynamics
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  • ISBN 978-3-319-65467-6
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About this book

This book presents several fundamental results in solving nonlinear reaction-diffusion equations and systems using symmetry-based methods. Reaction-diffusion systems are fundamental modeling tools for mathematical biology with applications to ecology, population dynamics, pattern formation, morphogenesis, enzymatic reactions and chemotaxis. The book discusses the properties of nonlinear reaction-diffusion systems, which are relevant for biological applications, from the symmetry point of view, providing rigorous definitions and constructive algorithms to search for conditional symmetry (a nontrivial generalization of the well-known Lie symmetry) of nonlinear reaction-diffusion systems. In order to present applications to population dynamics, it focuses mainly on two- and three-component diffusive Lotka-Volterra systems. While it is primarily a valuable guide for researchers working with reaction-diffusion systems  and those developing the theoretical aspects of conditional symmetry conception, parts of the book can also be used in master’s level mathematical biology courses.

About the authors

Roman Cherniha graduated in mathematics from the Taras Shevchenko Kyiv State University (1981), and defended his PhD dissertation (1987) and habilitation (2003) at the Institute of Mathematics, NAS of Ukraine. During his early career, he gained substantial experience on the field of applied mathematics and physics at the Institute of Technical Heat Physics (Kyiv). Since 1992, he has held a permanent position at the Institute of Mathematics. He spent a few years abroad working at the Henri Poincaré Unniversity (a temporary CNRS position) and the University of Nottingham (Marie Curie Research Fellow). He has a wide range of research interests including: non-linear partial differential equations (especially reaction-diffusion equations): Lie and conditional symmetries, exact solutions and their properties; development of new methods for analytically solving non-linear PDEs; application of modern methods for analytically solving nonlinear boundary-value problems arising in  real world application; analytically  and numerically  solving boundary-value problems with free boundaries; development of mathematical models describing the specific processes arising in physics, biology and medicine.

Vasyl’ Davydovych   graduated in mathematics from the Lesya Ukrainka  Volyn National  University (2009),  and defended his PhD dissertation (2014) at the  Institute of Mathematics,  NAS of Ukraine. At present, he is a junior researcher at the Institute of Mathematics at the NAS of Ukraine. He is currently investigating nonlinear PDEs using symmetry-based methods. His primary aim is the study of nonlinear reaction-diffusion systems arising in real-world applications (such as the diffusive Lotka-Volterra  type systems).

Table of contents (4 chapters)

  • Scalar Reaction-Diffusion Equations: Conditional Symmetry, Exact Solutions and Applications

    Cherniha, Roman (et al.)

    Pages 1-44

  • Q-Conditional Symmetries of Reaction-Diffusion Systems

    Cherniha, Roman (et al.)

    Pages 45-76

  • Conditional Symmetries and Exact Solutions of Diffusive Lotka–Volterra Systems

    Cherniha, Roman (et al.)

    Pages 77-118

  • Q-Conditional Symmetries of the First Type and Exact Solutions of Nonlinear Reaction-Diffusion Systems

    Cherniha, Roman (et al.)

    Pages 119-154

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-65467-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA
  • ISBN 978-3-319-65465-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Nonlinear Reaction-Diffusion Systems
Book Subtitle
Conditional Symmetry, Exact Solutions and their Applications in Biology
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2196
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-65467-6
DOI
10.1007/978-3-319-65467-6
Softcover ISBN
978-3-319-65465-2
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XIII, 160
Number of Illustrations and Tables
3 b/w illustrations, 10 illustrations in colour
Topics