Asymptotic Spreading for General Heterogeneous Fisher-KPP Type Equations
Author: Henri Berestycki
Publisher: American Mathematical Society
Published: 2022-11-10
Total Pages: 282
ISBN-13: 1470454297
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Author: Henri Berestycki
Publisher: American Mathematical Society
Published: 2022-11-10
Total Pages: 282
ISBN-13: 1470454297
DOWNLOAD EBOOK →View the abstract.
Author: King-Yeung Lam
Publisher: Springer Nature
Published: 2022-12-01
Total Pages: 316
ISBN-13: 3031204220
DOWNLOAD EBOOK →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.
Author: Nassif Ghoussoub
Publisher: American Mathematical Society
Published: 2023-05-23
Total Pages: 138
ISBN-13: 1470461196
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Author: Giao Ky Duong
Publisher: American Mathematical Society
Published: 2023-05-23
Total Pages: 104
ISBN-13: 1470461218
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Author: Mohandas Pillai
Publisher: American Mathematical Society
Published: 2023-04-07
Total Pages: 254
ISBN-13: 1470459930
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Author: André Gil Henriques
Publisher: American Mathematical Society
Published: 2023-02-13
Total Pages: 100
ISBN-13: 1470455404
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Author: Philipp Grohs
Publisher: American Mathematical Society
Published: 2023-04-07
Total Pages: 106
ISBN-13: 147045632X
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Author: Kihyun Kim
Publisher: American Mathematical Society
Published: 2023-04-07
Total Pages: 140
ISBN-13: 147046120X
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Author: Martin Herschend
Publisher: American Mathematical Society
Published: 2023-05-23
Total Pages: 156
ISBN-13: 1470456311
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Author: James East
Publisher: American Mathematical Society
Published: 2023-04-07
Total Pages: 144
ISBN-13: 1470462699
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