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＜電子ブック＞
Nonlinear Reaction-Diffusion Systems : Conditional Symmetry, Exact Solutions and their Applications in Biology / by Roman Cherniha, Vasyl' Davydovych
(Lecture Notes in Mathematics. ISSN:16179692 ; 2196)

版	1st ed. 2017.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2017
本文言語	英語
大きさ	XIII, 160 p. 13 illus., 10 illus. in color : online resource
著者標目	*Cherniha, Roman author Davydovych, Vasyl' author SpringerLink (Online service)
件　名	LCSH:Biomathematics LCSH:Differential equations LCSH:Mathematical physics FREE:Mathematical and Computational Biology FREE:Differential Equations FREE:Mathematical Physics
一般注記	1 Scalar reaction-diffusion equations – conditional symmetry, exact solutions and applications -- 2 Q-conditional symmetries of reaction-diffusion systems -- 3 Conditional symmetries and exact solutions of diffusive Lotka–Volterra systems -- 4 Q-conditional symmetries of the first type and exact solutions of nonlinear reaction-diffusion systems -- A List of reaction-diffusion systems and exact solutions -- Index 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 HTTP:URL=https://doi.org/10.1007/978-3-319-65467-6

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