Geometric Theory of Singular Phenomena in Partial Differential Equations PDF Download

Author: Jean Pierre Bourguignon
Publisher: Cambridge University Press
ISBN: 9780521632461
Category : Mathematics
Languages : en
Pages : 198

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Book Description
This book gathers together papers from a workshop held in Cortona, Italy. The contributions come from a group of outstanding mathematicians and together they cover the most recent advances in the geometric theory of singular phenomena of partial differential equations occurring in real and complex differential geometry. This volume will be of great interest to all those whose research interests lie in real and complex differential geometry, partial differential equations, and gauge theory.

Author: Walter A. Strauss
Publisher: John Wiley & Sons
ISBN: 0470054565
Category : Mathematics
Languages : en
Pages : 467

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Book Description
Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

Author: Rajendra Bhatia
Publisher: World Scientific
ISBN: 9814462934
Category : Mathematics
Languages : en
Pages : 4137

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Book Description
ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.

Author: Pierre Albin
Publisher: American Mathematical Soc.
ISBN: 1470410435
Category : Mathematics
Languages : en
Pages : 378

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Book Description
In 2012, the Centre de Recherches Mathématiques was at the center of many interesting developments in geometric and spectral analysis, with a thematic program on Geometric Analysis and Spectral Theory followed by a thematic year on Moduli Spaces, Extremality and Global Invariants. This volume contains original contributions as well as useful survey articles of recent developments by participants from three of the workshops organized during these programs: Geometry of Eigenvalues and Eigenfunctions, held from June 4-8, 2012; Manifolds of Metrics and Probabilistic Methods in Geometry and Analysis, held from July 2-6, 2012; and Spectral Invariants on Non-compact and Singular Spaces, held from July 23-27, 2012. The topics covered in this volume include Fourier integral operators, eigenfunctions, probability and analysis on singular spaces, complex geometry, Kähler-Einstein metrics, analytic torsion, and Strichartz estimates. This book is co-published with the Centre de Recherches Mathématiques.

Author: Frank Pacard
Publisher: Springer Science & Business Media
ISBN: 146121386X
Category : Mathematics
Languages : en
Pages : 342

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Book Description
Aimed at mathematicians, physicists, engineers, and grad students, this monograph will be useful for the nonlinear analysis of problems arising in geometry or mathematical physics. The material presented covers recent and original results by the authors, and serves as an excellent classroom text or a valuable self-study resource.

Author: Jürgen Jost
Publisher: American Mathematical Soc.
ISBN: 0821843362
Category : Mathematics
Languages : en
Pages : 110

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Book Description
This book presents a mathematical treatment of Bosonic string theory from the point of view of global geometry. As motivation, Jost presents the theory of point particles and Feynman path integrals. He provides detailed background material, including the geometry of Teichmuller space, the conformal and complex geometry of Riemann surfaces, and the subtleties of boundary regularity questions. The high point is the description of the partition function for Bosonic strings as a finite-dimensional integral over a moduli space of Riemann surfaces. Jost concludes with some topics related to open and closed strings and $D$-branes. Bosonic Strings is suitable for graduate students and researchers interested in the mathematics underlying string theory.

Author: David Colton
Publisher: Springer Science & Business Media
ISBN: 3662035375
Category : Science
Languages : en
Pages : 347

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Book Description
This book is devoted to the mathematical and numerical analysis of the inverse scattering problem for acoustic and electromagnetic waves. The second edition includes material on Newton’s method for the inverse obstacle problem, an elegant proof of uniqueness for the inverse medium problem, a discussion of the spectral theory of the far field operator and a method for determining the support of an inhomogeneous medium from far field data.

Author: Andreas Kirsch
Publisher: Springer Science & Business Media
ISBN: 9780387945309
Category : Science
Languages : en
Pages : 304

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Book Description
Following Keller [119] we call two problems inverse to each other if the for mulation of each of them requires full or partial knowledge of the other. By this definition, it is obviously arbitrary which of the two problems we call the direct and which we call the inverse problem. But usually, one of the problems has been studied earlier and, perhaps, in more detail. This one is usually called the direct problem, whereas the other is the inverse problem. However, there is often another, more important difference between these two problems. Hadamard (see [91]) introduced the concept of a well-posed problem, originating from the philosophy that the mathematical model of a physical problem has to have the properties of uniqueness, existence, and stability of the solution. If one of the properties fails to hold, he called the problem ill-posed. It turns out that many interesting and important inverse in science lead to ill-posed problems, while the corresponding di problems rect problems are well-posed. Often, existence and uniqueness can be forced by enlarging or reducing the solution space (the space of "models"). For restoring stability, however, one has to change the topology of the spaces, which is in many cases impossible because of the presence of measurement errors. At first glance, it seems to be impossible to compute the solution of a problem numerically if the solution of the problem does not depend continuously on the data, i. e. , for the case of ill-posed problems.

Author: Odo Diekmann
Publisher: Springer Science & Business Media
ISBN: 1461242061
Category : Mathematics
Languages : en
Pages : 547

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Book Description
The aim here is to provide an introduction to the mathematical theory of infinite dimensional dynamical systems by focusing on a relatively simple - yet rich - class of examples, delay differential equations. This textbook contains detailed proofs and many exercises, intended both for self-study and for courses at graduate level, as well as a reference for basic results. As the subtitle indicates, this book is about concepts, ideas, results and methods from linear functional analysis, complex function theory, the qualitative theory of dynamical systems and nonlinear analysis. The book provides the reader with a working knowledge of applied functional analysis and dynamical systems.

Author: Jean-Claude Nedelec
Publisher: Springer Science & Business Media
ISBN: 1475743939
Category : Mathematics
Languages : en
Pages : 328

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Book Description
Acoustic and electromagnetic waves underlie a vast range of modern technology from sonar, radio, and television to microwave heating and electromagnetic compatibility analysis. Mathematical modeling of these waves has undergone considerable growth in recent years, and this timely book, written by a leading international researcher, presents the research in a careful and complete way.