Analysis of Singularities for Partial Differential Equations
Title | Analysis of Singularities for Partial Differential Equations PDF eBook |
Author | Shuxing Chen |
Publisher | World Scientific |
Pages | 207 |
Release | 2011 |
Genre | Mathematics |
ISBN | 9814304832 |
The book provides a comprehensive overview on the theory on analysis of singularities for partial differential equations (PDEs). It contains a summarization of the formation, development and main results on this topic. Some of the author's discoveries and original contributions are also included, such as the propagation of singularities of solutions to nonlinear equations, singularity index and formation of shocks.
Seminar on Singularities of Solutions of Linear Partial Differential Equations
Title | Seminar on Singularities of Solutions of Linear Partial Differential Equations PDF eBook |
Author | George F. Oster |
Publisher | Princeton University Press |
Pages | 295 |
Release | 1978 |
Genre | Mathematics |
ISBN | 0691082138 |
Singularities of solutions of differential equations forms the common theme of these papers taken from a seminar held at the Institute for Advanced Study in Princeton in 1977-1978. While some of the lectures were devoted to the analysis of singularities, others focused on applications in spectral theory. As an introduction to the subject, this volume treats current research in the field in such a way that it can be studied with profit by the non-specialist.
Singularities in PDE and the Calculus of Variations
Title | Singularities in PDE and the Calculus of Variations PDF eBook |
Author | Stanley Alama |
Publisher | American Mathematical Soc. |
Pages | 284 |
Release | |
Genre | Mathematics |
ISBN | 9780821873311 |
This book contains papers presented at the "Workshop on Singularities in PDE and the Calculus of Variations" at the CRM in July 2006. The main theme of the meeting was the formation of geometrical singularities in PDE problems with a variational formulation. These equations typically arise in some applications (to physics, engineering, or biology, for example) and their resolution often requires a combination of methods coming from areas such as functional and harmonic analysis, differential geometry and geometric measure theory. Among the PDE problems discussed were: the Cahn-Hilliard model of phase transitions and domain walls; vortices in Ginzburg-Landau type models for superconductivity and superfluidity; the Ohna-Kawasaki model for di-block copolymers; models of image enhancement; and Monge-Ampere functions. The articles give a sampling of problems and methods in this diverse area of mathematics, which touches a large part of modern mathematics and its applications.
Seminar on Singularities of Solutions of Linear Partial Differential Equations. (AM-91), Volume 91
Title | Seminar on Singularities of Solutions of Linear Partial Differential Equations. (AM-91), Volume 91 PDF eBook |
Author | Lars Hörmander |
Publisher | Princeton University Press |
Pages | 296 |
Release | 2016-03-02 |
Genre | Mathematics |
ISBN | 1400881587 |
Singularities of solutions of differential equations forms the common theme of these papers taken from a seminar held at the Institute for Advanced Study in Princeton in 1977-1978. While some of the lectures were devoted to the analysis of singularities, others focused on applications in spectral theory. As an introduction to the subject, this volume treats current research in the field in such a way that it can be studied with profit by the non-specialist.
Approaches to Singular Analysis
Title | Approaches to Singular Analysis PDF eBook |
Author | Juan B. Gil |
Publisher | Birkhäuser |
Pages | 264 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 303488253X |
This collection presents various approaches to analytic problems that arise in the context of singular spaces. It contains articles offering introductions to various pseudodifferential calculi and discussions of relations between them, plus invited papers from mathematicians who have made significant contributions to this field
Singularities: Formation, Structure, and Propagation
Title | Singularities: Formation, Structure, and Propagation PDF eBook |
Author | J. Eggers |
Publisher | Cambridge University Press |
Pages | 471 |
Release | 2015-09-10 |
Genre | Mathematics |
ISBN | 1316352390 |
Many key phenomena in physics and engineering are described as singularities in the solutions to the differential equations describing them. Examples covered thoroughly in this book include the formation of drops and bubbles, the propagation of a crack and the formation of a shock in a gas. Aimed at a broad audience, this book provides the mathematical tools for understanding singularities and explains the many common features in their mathematical structure. Part I introduces the main concepts and techniques, using the most elementary mathematics possible so that it can be followed by readers with only a general background in differential equations. Parts II and III require more specialised methods of partial differential equations, complex analysis and asymptotic techniques. The book may be used for advanced fluid mechanics courses and as a complement to a general course on applied partial differential equations.
Methods Of Geometry In The Theory Of Partial Differential Equations: Principle Of The Cancellation Of Singularities
Title | Methods Of Geometry In The Theory Of Partial Differential Equations: Principle Of The Cancellation Of Singularities PDF eBook |
Author | Takashi Suzuki |
Publisher | World Scientific |
Pages | 414 |
Release | 2024-01-22 |
Genre | Mathematics |
ISBN | 9811287910 |
Mathematical models are used to describe the essence of the real world, and their analysis induces new predictions filled with unexpected phenomena.In spite of a huge number of insights derived from a variety of scientific fields in these five hundred years of the theory of differential equations, and its extensive developments in these one hundred years, several principles that ensure these successes are discovered very recently.This monograph focuses on one of them: cancellation of singularities derived from interactions of multiple species, which is described by the language of geometry, in particular, that of global analysis.Five objects of inquiry, scattered across different disciplines, are selected in this monograph: evolution of geometric quantities, models of multi-species in biology, interface vanishing of d - δ systems, the fundamental equation of electro-magnetic theory, and free boundaries arising in engineering.The relaxation of internal tensions in these systems, however, is described commonly by differential forms, and the reader will be convinced of further applications of this principle to other areas.