國立虎尾科技大學 |

Introduction to Reaction-Diffusion Equations = Theory and Applications to Spatial Ecology and Evolutionary Biology /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Introduction to Reaction-Diffusion Equations/ by King-Yeung Lam, Yuan Lou.
Reminder of title:	Theory and Applications to Spatial Ecology and Evolutionary Biology /
Author:	Lam, King-Yeung.
other author:	Lou, Yuan.
Description:	XVI, 312 p. 1 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Mathematical analysis. -
Online resource:	https://doi.org/10.1007/978-3-031-20422-7
ISBN:	9783031204227

Introduction to Reaction-Diffusion Equations = Theory and Applications to Spatial Ecology and Evolutionary Biology /
Lam, King-Yeung.

Introduction to Reaction-Diffusion EquationsTheory and Applications to Spatial Ecology and Evolutionary Biology /[electronic resource] :by King-Yeung Lam, Yuan Lou. - 1st ed. 2022. - XVI, 312 p. 1 illus.online resource. - Lecture Notes on Mathematical Modelling in the Life Sciences,2193-4797. - Lecture Notes on Mathematical Modelling in the Life Sciences,.

Part I Linear Theory -- 1. The Maximum Principle and the Principal Eigenvalues for Single Equations -- 2. The Principal Eigenvalue for Periodic-Parabolic Problems -- 3. The Maximum Principle and the Principal Eigenvalue for Systems -- 4. The Principal Floquet Bundle for Parabolic Equations -- Part II Ecological Dynamics -- 5. The Logistic Equation With Diffusion -- 6. Spreading in Homogeneous and Shifting Environments -- 7. The Lotka–Volterra Competition-Diffusion Systems for Two Species -- 8. Dynamics of Phytoplankton Populations -- Part III Evolutionary Dynamics -- 9. Elements of Adaptive Dynamics -- 10. Selection-Mutation Models -- Part IV Appendices -- A. The Fixed Point Index -- B. The Krein–Rutman Theorem -- C. Subhomogeneous Dynamics -- D. Existence of Connecting Orbits -- E. Abstract Competition Systems in Ordered Banach Spaces -- Index.

This book introduces some basic mathematical tools in reaction-diffusion models, with applications to spatial ecology and evolutionary biology. It is divided into four parts. The first part is an introduction to the maximum principle, the theory of principal eigenvalues for elliptic and periodic-parabolic equations and systems, and the theory of principal Floquet bundles. The second part concerns the applications in spatial ecology. We discuss the dynamics of a single species and two competing species, as well as some recent progress on N competing species in bounded domains. Some related results on stream populations and phytoplankton populations are also included. We also discuss the spreading properties of a single species in an unbounded spatial domain, as modeled by the Fisher-KPP equation. The third part concerns the applications in evolutionary biology. We describe the basic notions of adaptive dynamics, such as evolutionarily stable strategies and evolutionary branching points, in the context of a competition model of stream populations. We also discuss a class of selection-mutation models describing a population structured along a continuous phenotypical trait. The fourth part consists of several appendices, which present a self-contained treatment of some basic abstract theories in functional analysis and dynamical systems. Topics include the Krein-Rutman theorem for linear and nonlinear operators, as well as some elements of monotone dynamical systems and abstract competition systems. Most of the book is self-contained and it is aimed at graduate students and researchers who are interested in the theory and applications of reaction-diffusion equations.

ISBN: 9783031204227

Standard No.: 10.1007/978-3-031-20422-7doiSubjects--Topical Terms:

527926
Mathematical analysis.

LC Class. No.: QA299.6-433

Dewey Class. No.: 515

Introduction to Reaction-Diffusion Equations = Theory and Applications to Spatial Ecology and Evolutionary Biology /
LDR:04004nam a22003975i 4500 001 1086146
003 DE-He213
005 20221201125437.0
007 cr nn 008mamaa
008 221228s2022 sz | s |||| 0|eng d
020 $a 9783031204227 $9 978-3-031-20422-7
024 7 $a 10.1007/978-3-031-20422-7 $2 doi
035 $a 978-3-031-20422-7
050 4 $a QA299.6-433
072 7 $a PBK $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBK $2 thema
082 0 4 $a 515 $2 23
100 1 $a Lam, King-Yeung. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1392837
245 1 0 $a Introduction to Reaction-Diffusion Equations $h [electronic resource] : $b Theory and Applications to Spatial Ecology and Evolutionary Biology / $c by King-Yeung Lam, Yuan Lou.
250 $a 1st ed. 2022.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a XVI, 312 p. 1 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Lecture Notes on Mathematical Modelling in the Life Sciences, $x 2193-4797
505 0 $a Part I Linear Theory -- 1. The Maximum Principle and the Principal Eigenvalues for Single Equations -- 2. The Principal Eigenvalue for Periodic-Parabolic Problems -- 3. The Maximum Principle and the Principal Eigenvalue for Systems -- 4. The Principal Floquet Bundle for Parabolic Equations -- Part II Ecological Dynamics -- 5. The Logistic Equation With Diffusion -- 6. Spreading in Homogeneous and Shifting Environments -- 7. The Lotka–Volterra Competition-Diffusion Systems for Two Species -- 8. Dynamics of Phytoplankton Populations -- Part III Evolutionary Dynamics -- 9. Elements of Adaptive Dynamics -- 10. Selection-Mutation Models -- Part IV Appendices -- A. The Fixed Point Index -- B. The Krein–Rutman Theorem -- C. Subhomogeneous Dynamics -- D. Existence of Connecting Orbits -- E. Abstract Competition Systems in Ordered Banach Spaces -- Index.
520 $a This book introduces some basic mathematical tools in reaction-diffusion models, with applications to spatial ecology and evolutionary biology. It is divided into four parts. The first part is an introduction to the maximum principle, the theory of principal eigenvalues for elliptic and periodic-parabolic equations and systems, and the theory of principal Floquet bundles. The second part concerns the applications in spatial ecology. We discuss the dynamics of a single species and two competing species, as well as some recent progress on N competing species in bounded domains. Some related results on stream populations and phytoplankton populations are also included. We also discuss the spreading properties of a single species in an unbounded spatial domain, as modeled by the Fisher-KPP equation. The third part concerns the applications in evolutionary biology. We describe the basic notions of adaptive dynamics, such as evolutionarily stable strategies and evolutionary branching points, in the context of a competition model of stream populations. We also discuss a class of selection-mutation models describing a population structured along a continuous phenotypical trait. The fourth part consists of several appendices, which present a self-contained treatment of some basic abstract theories in functional analysis and dynamical systems. Topics include the Krein-Rutman theorem for linear and nonlinear operators, as well as some elements of monotone dynamical systems and abstract competition systems. Most of the book is self-contained and it is aimed at graduate students and researchers who are interested in the theory and applications of reaction-diffusion equations.
650 0 $a Mathematical analysis. $3 527926
650 0 $a Evolution (Biology). $3 686236
650 0 $a Mathematics. $3 527692
650 0 $a Population genetics. $3 527720
650 0 $a Dynamical systems. $3 1249739
650 1 4 $a Analysis. $3 669490
650 2 4 $a Evolutionary Biology. $3 668573
650 2 4 $a Applications of Mathematics. $3 669175
650 2 4 $a Population Genetics. $3 1392839
650 2 4 $a Dynamical Systems. $3 1366074
700 1 $a Lou, Yuan. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1392838
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783031204210
776 0 8 $i Printed edition: $z 9783031204234
830 0 $a Lecture Notes on Mathematical Modelling in the Life Sciences, $x 2193-4789 $3 1261085
856 4 0 $u https://doi.org/10.1007/978-3-031-20422-7
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)