Nonlinear Dynamics and Evolution Equations

Nonlinear Dynamics and Evolution Equations
Author: Hermann Brunner
Publisher: American Mathematical Soc.
Total Pages: 322
Release: 2006
Genre: Mathematics
ISBN: 0821837214

The papers in this volume reflect a broad spectrum of current research activities on the theory and applications of nonlinear dynamics and evolution equations. They are based on lectures given during the International Conference on Nonlinear Dynamics and Evolution Equations at Memorial University of Newfoundland, St. John's, NL, Canada, July 6-10, 2004. This volume contains thirteen invited and refereed papers. Nine of these are survey papers, introducing the reader to, anddescribing the current state of the art in major areas of dynamical systems, ordinary, functional and partial differential equations, and applications of such equations in the mathematical modelling of various biological and physical phenomena. These papers are complemented by four research papers thatexamine particular problems in the theory and applications of dynamical systems. Information for our distributors: Titles in this series are copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

Handbook of Differential Equations: Stationary Partial Differential Equations

Handbook of Differential Equations: Stationary Partial Differential Equations
Author: Michel Chipot
Publisher: Elsevier
Total Pages: 618
Release: 2011-08-11
Genre: Mathematics
ISBN: 0080560598

This handbook is the sixth and last volume in the series devoted to stationary partial differential equations. The topics covered by this volume include in particular domain perturbations for boundary value problems, singular solutions of semilinear elliptic problems, positive solutions to elliptic equations on unbounded domains, symmetry of solutions, stationary compressible Navier-Stokes equation, Lotka-Volterra systems with cross-diffusion, and fixed point theory for elliptic boundary value problems.* Collection of self-contained, state-of-the-art surveys* Written by well-known experts in the field* Informs and updates on all the latest developments

Stable Solutions of Elliptic Partial Differential Equations

Stable Solutions of Elliptic Partial Differential Equations
Author: Louis Dupaigne
Publisher: CRC Press
Total Pages: 334
Release: 2011-03-15
Genre: Mathematics
ISBN: 1420066552

Stable solutions are ubiquitous in differential equations. They represent meaningful solutions from a physical point of view and appear in many applications, including mathematical physics (combustion, phase transition theory) and geometry (minimal surfaces). Stable Solutions of Elliptic Partial Differential Equations offers a self-contained presentation of the notion of stability in elliptic partial differential equations (PDEs). The central questions of regularity and classification of stable solutions are treated at length. Specialists will find a summary of the most recent developments of the theory, such as nonlocal and higher-order equations. For beginners, the book walks you through the fine versions of the maximum principle, the standard regularity theory for linear elliptic equations, and the fundamental functional inequalities commonly used in this field. The text also includes two additional topics: the inverse-square potential and some background material on submanifolds of Euclidean space.

Nonlinear Functional Analysis and its Applications

Nonlinear Functional Analysis and its Applications
Author: E. Zeidler
Publisher: Springer Science & Business Media
Total Pages: 1007
Release: 2013-12-01
Genre: Mathematics
ISBN: 1461245664

The fourth of a five-volume exposition of the main principles of nonlinear functional analysis and its applications to the natural sciences, economics, and numerical analysis. The presentation is self-contained and accessible to the non-specialist, and topics covered include applications to mechanics, elasticity, plasticity, hydrodynamics, thermodynamics, statistical physics, and special and general relativity including cosmology. The book contains a detailed physical motivation of the relevant basic equations and a discussion of particular problems which have played a significant role in the development of physics and through which important mathematical and physical insight may be gained. It combines classical and modern ideas to build a bridge between the language and thoughts of physicists and mathematicians. Many exercises and a comprehensive bibliography complement the text.

Abelian Coverings of the Complex Projective Plane Branched along Configurations of Real Lines

Abelian Coverings of the Complex Projective Plane Branched along Configurations of Real Lines
Author: Eriko Hironaka
Publisher: American Mathematical Soc.
Total Pages: 98
Release: 1993
Genre: Mathematics
ISBN: 082182564X

This work studies abelian branched coverings of smooth complex projective surfaces from the topological viewpoint. Geometric information about the coverings (such as the first Betti numbers of a smooth model or intersections of embedded curves) is related to topological and combinatorial information about the base space and branch locus. Special attention is given to examples in which the base space is the complex projective plane and the branch locus is a configuration of lines.

Duality and Definability in First Order Logic

Duality and Definability in First Order Logic
Author: Michael Makkai
Publisher: American Mathematical Soc.
Total Pages: 122
Release: 1993
Genre: Mathematics
ISBN: 0821825658

We develop a duality theory for small Boolean pretoposes in which the dual of the [italic capital]T is the groupoid of models of a Boolean pretopos [italic capital]T equipped with additional structure derived from ultraproducts. The duality theorem states that any small Boolean pretopos is canonically equivalent to its double dual. We use a strong version of the duality theorem to prove the so-called descent theorem for Boolean pretoposes which says that category of descent data derived from a conservative pretopos morphism between Boolean pretoposes is canonically equivalent to the domain-pretopos. The descent theorem contains the Beth definability theorem for classical first order logic. Moreover, it gives, via the standard translation from the language of categories to symbolic logic, a new definability theorem for classical first order logic concerning set-valued functors on models, expressible in purely syntactical (arithmetical) terms.

Harmonic Analysis for Anisotropic Random Walks on Homogeneous Trees

Harmonic Analysis for Anisotropic Random Walks on Homogeneous Trees
Author: Alessandro FigĂ -Talamanca
Publisher: American Mathematical Soc.
Total Pages: 86
Release: 1994
Genre: Mathematics
ISBN: 0821825941

This work presents a detailed study of the anisotropic series representations of the free product group Z/2Z*...*Z/2Z. These representations are infinite dimensional, irreducible, and unitary and can be divided into principal and complementary series. Anisotropic series representations are interesting because, while they are not restricted from any larger continuous group in which the discrete group is a lattice, they nonetheless share many properties of such restrictions. The results of this work are also valid for nonabelian free groups on finitely many generators.

A Topological Chern-Weil Theory

A Topological Chern-Weil Theory
Author: Anthony Valiant Phillips
Publisher: American Mathematical Soc.
Total Pages: 90
Release: 1993
Genre: Mathematics
ISBN: 0821825666

We examine the general problem of computing characteristic invariants of principal bundles whose structural group [italic capital]G is a topological group. Under the hypothesis that [italic capital]G has real cohomology finitely generated as an [bold]R-module, we are able to give a completely topological, local method for computing representative cocycles for real characteristic classes; our method applies, for example, to the (homologically) 10-dimensional non-Lie group of Hilton-Roitberg-Stasheff.