Asymptotic Spreading for General Heterogeneous Fisher-KPP Type Equations PDF Download
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Author: Henri Berestycki
Publisher: American Mathematical Society
ISBN: 1470454297
Category : Mathematics
Languages : en
Pages : 282
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Book Description
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Author: Henri Berestycki
Publisher: American Mathematical Society
ISBN: 1470454297
Category : Mathematics
Languages : en
Pages : 282
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Book Description
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Author: King-Yeung Lam
Publisher: Springer Nature
ISBN: 3031204220
Category : Mathematics
Languages : en
Pages : 316
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Book Description
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: Tiago J. Fonseca
Publisher: American Mathematical Society
ISBN: 147046019X
Category : Mathematics
Languages : en
Pages : 158
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Author: Nassif Ghoussoub
Publisher: American Mathematical Society
ISBN: 1470461196
Category : Mathematics
Languages : en
Pages : 138
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Author: Giao Ky Duong
Publisher: American Mathematical Society
ISBN: 1470461218
Category : Mathematics
Languages : en
Pages : 104
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Author: Mohandas Pillai
Publisher: American Mathematical Society
ISBN: 1470459930
Category : Mathematics
Languages : en
Pages : 254
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Author: André Gil Henriques
Publisher: American Mathematical Society
ISBN: 1470455404
Category : Mathematics
Languages : en
Pages : 100
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Author: Sebastian Casalaina-Martin
Publisher: American Mathematical Society
ISBN: 1470460203
Category : Mathematics
Languages : en
Pages : 112
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Author: Guozhen Lu
Publisher: American Mathematical Society
ISBN: 1470455374
Category : Mathematics
Languages : en
Pages : 100
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Author: Srikanth B. Iyengar
Publisher: American Mathematical Society
ISBN: 1470471590
Category : Mathematics
Languages : en
Pages : 108
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Book Description
This book is aimed to provide an introduction to local cohomology which takes cognizance of the breadth of its interactions with other areas of mathematics. It covers topics such as the number of defining equations of algebraic sets, connectedness properties of algebraic sets, connections to sheaf cohomology and to de Rham cohomology, Gröbner bases in the commutative setting as well as for $D$-modules, the Frobenius morphism and characteristic $p$ methods, finiteness properties of local cohomology modules, semigroup rings and polyhedral geometry, and hypergeometric systems arising from semigroups. The book begins with basic notions in geometry, sheaf theory, and homological algebra leading to the definition and basic properties of local cohomology. Then it develops the theory in a number of different directions, and draws connections with topology, geometry, combinatorics, and algorithmic aspects of the subject.
