Nonlinear Reaction-Diffusion Systems : Conditional Symmetry, Exact Solutions and their Applications in Biology

Roman Cherniha

ISBN 10: 3319654659 / ISBN 13: 9783319654652

Published by Springer, Springer, 2017

About this Item

Druck auf Anfrage Neuware - Printed after ordering - This book presents several fundamental results insolving 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, whichare relevant for biological applications,from the symmetry point of view, providing rigorous definitionsand constructive algorithmstosearch for conditional symmetry (a nontrivial generalization of the well-known Lie symmetry)ofnonlinear reaction-diffusion systems. In order to presentapplications to population dynamics,it focuses mainlyontwo- and three-component diffusive Lotka-Volterra systems.While it is primarily a valuable guideforresearchers 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.

Seller Inventory # 9783319654652

Bibliographic Details

• Title: Nonlinear Reaction-Diffusion Systems : Conditional Symmetry, Exact Solutions and their Applications in Biology
• Publisher: Springer, Springer
• Publication Date: 2017
• Language: English
• ISBN 10: 3319654659
• ISBN 13: 9783319654652
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 10D millimeters 235 millimeters width by 155 millimeters height by 10 millimeters depth
• Weight: 277 grams

About this title

Synopsis

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

About the Author

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).