Author: Henri BerestyckiPublisher: American Mathematical Society
ISBN: 1470454297
Category : Mathematics
Languages : en
Pages : 282
Book Description
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Asymptotic Spreading for General Heterogeneous Fisher-KPP Type Equations
Author: Henri BerestyckiPublisher: American Mathematical Society
ISBN: 1470454297
Category : Mathematics
Languages : en
Pages : 282
Book Description
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Introduction to Reaction-Diffusion Equations
Author: King-Yeung LamPublisher: Springer Nature
ISBN: 3031204220
Category : Mathematics
Languages : en
Pages : 316
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.
Multiplicity and Stability of the Pohozaev Obstruction for Hardy-Schrödinger Equations with Boundary Singularity
Author: Nassif GhoussoubPublisher: American Mathematical Society
ISBN: 1470461196
Category : Mathematics
Languages : en
Pages : 138
Book Description
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Construction of Blowup Solutions for the Complex Ginzburg-Landau Equation with Critical Parameters
Author: Giao Ky DuongPublisher: American Mathematical Society
ISBN: 1470461218
Category : Mathematics
Languages : en
Pages : 104
Book Description
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Infinite Time Blow-Up Solutions to the Energy Critical Wave Maps Equation
Author: Mohandas PillaiPublisher: American Mathematical Society
ISBN: 1470459930
Category : Mathematics
Languages : en
Pages : 254
Book Description
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Planar Algebras in Braided Tensor Categories
Author: André Gil HenriquesPublisher: American Mathematical Society
ISBN: 1470455404
Category : Mathematics
Languages : en
Pages : 100
Book Description
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A Proof that Artificial Neural Networks Overcome the Curse of Dimensionality in the Numerical Approximation of Black–Scholes Partial Differential Equations
Author: Philipp GrohsPublisher: American Mathematical Society
ISBN: 147045632X
Category : Mathematics
Languages : en
Pages : 106
Book Description
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On Pseudoconformal Blow-Up Solutions to the Self-Dual Chern-Simons-Schrödinger Equation: Existence, Uniqueness, and Instability
Author: Kihyun KimPublisher: American Mathematical Society
ISBN: 147046120X
Category : Mathematics
Languages : en
Pages : 140
Book Description
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Representation Theory of Geigle-Lenzing Complete Intersections
Author: Martin HerschendPublisher: American Mathematical Society
ISBN: 1470456311
Category : Mathematics
Languages : en
Pages : 156
Book Description
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Congruence Lattices of Ideals in Categories and (Partial) Semigroups
Author: James EastPublisher: American Mathematical Society
ISBN: 1470462699
Category : Mathematics
Languages : en
Pages : 144
Book Description
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