Methods Of Geometry In The Theory Of Partial Differential Equations Principle Of The Cancellation Of Singularities
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Methods Of Geometry In The Theory Of Partial Differential Equations Principle Of The Cancellation Of Singularities
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Author : Takashi Suzuki
language : en
Publisher: World Scientific
Release Date : 2024-01-22
Methods Of Geometry In The Theory Of Partial Differential Equations Principle Of The Cancellation Of Singularities written by Takashi Suzuki and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-22 with Mathematics categories.
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.
Typical Singularities Of Differential 1 Forms And Pfaffian Equations
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Author : Mikhail Zhitomirskiĭ
language : en
Publisher: American Mathematical Soc.
Release Date : 1992
Typical Singularities Of Differential 1 Forms And Pfaffian Equations written by Mikhail Zhitomirskiĭ and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
Singularities and the classification of 1-forms and Pfaffian equations are interesting not only as classical problems, but also because of their applications in contact geometry, partial differential equations, control theory, nonholonomic dynamics, and variational problems. In addition to collecting results on the geometry of singularities and classification of differential forms and Pfaffian equations, this monograph discusses applications and closely related classification problems. Zhitomirskii presents proofs with all results and ends each chapter with a summary of the main results, a tabulation of the singularities, and a list of the normal forms. The main results of the book are also collected together in the introduction.
Geometry And Arithmetic Around Euler Partial Differential Equations
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Author : R.-P. Holzapfel
language : en
Publisher: Springer
Release Date : 1986-08-31
Geometry And Arithmetic Around Euler Partial Differential Equations written by R.-P. Holzapfel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-08-31 with Mathematics categories.
Applied Mechanics Reviews
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Author :
language : en
Publisher:
Release Date : 1992
Applied Mechanics Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mechanics, Applied categories.
Partial Differential Equations
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Author : Walter A. Strauss
language : en
Publisher: John Wiley & Sons
Release Date : 2007-12-21
Partial Differential Equations written by Walter A. Strauss and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-21 with Mathematics categories.
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.
A Domain Decomposition Method For Some Partial Differential Equations With Singularities
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Author : Charissa Chui-yee Cheung
language : en
Publisher:
Release Date : 1997
A Domain Decomposition Method For Some Partial Differential Equations With Singularities written by Charissa Chui-yee Cheung and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Decomposition method categories.
Singularities Of Differentiable Maps
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Author : V.I. Arnold
language : en
Publisher: Springer Science & Business Media
Release Date : 1985-01-01
Singularities Of Differentiable Maps written by V.I. Arnold and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-01-01 with Mathematics categories.
... there is nothing so enthralling, so grandiose, nothing that stuns or captivates the human soul quite so much as a first course in a science. After the first five or six lectures one already holds the brightest hopes, already sees oneself as a seeker after truth. I too have wholeheartedly pursued science passionately, as one would a beloved woman. I was a slave, and sought no other sun in my life. Day and night I crammed myself, bending my back, ruining myself over my books; I wept when I beheld others exploiting science fot personal gain. But I was not long enthralled. The truth is every science has a beginning, but never an end - they go on for ever like periodic fractions. Zoology, for example, has discovered thirty-five thousand forms of life ... A. P. Chekhov. "On the road" In this book a start is made to the "zoology" of the singularities of differentiable maps. This theory is a young branch of analysis which currently occupies a central place in mathematics; it is the crossroads of paths leading from very abstract corners of mathematics (such as algebraic and differential geometry and topology, Lie groups and algebras, complex manifolds, commutative algebra and the like) to the most applied areas (such as differential equations and dynamical systems, optimal control, the theory of bifurcations and catastrophes, short-wave and saddle-point asymptotics and geometrical and wave optics).
The Method Of Intrinsic Scaling
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Author : José Miguel Urbano
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-20
The Method Of Intrinsic Scaling written by José Miguel Urbano and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-20 with Mathematics categories.
This set of lectures, which had its origin in a mini course delivered at the Summer Program of IMPA (Rio de Janeiro), is an introduction to intrinsic scaling, a powerful method in the analysis of degenerate and singular PDEs.In the first part, the theory is presented from scratch for the model case of the degenerate p-Laplace equation. The second part deals with three applications of the theory to relevant models arising from flows in porous media and phase transitions.
Meshfree Methods For Partial Differential Equations Vii
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Author : Michael Griebel
language : en
Publisher: Springer
Release Date : 2014-12-02
Meshfree Methods For Partial Differential Equations Vii written by Michael Griebel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-02 with Mathematics categories.
Meshfree methods, particle methods, and generalized finite element methods have witnessed substantial development since the mid 1990s. The growing interest in these methods is due in part to the fact that they are extremely flexible numerical tools and can be interpreted in a number of ways. For instance, meshfree methods can be viewed as a natural extension of classical finite element and finite difference methods to scattered node configurations with no fixed connectivity. Furthermore, meshfree methods offer a number of advantageous features which are especially attractive when dealing with multiscale phenomena: a priori knowledge about particular local behavior of the solution can easily be introduced in the meshfree approximation space, and coarse-scale approximations can be seamlessly refined with fine-scale information. This volume collects selected papers presented at the Seventh International Workshop on Meshfree Methods, held in Bonn, Germany in September 2013. They address various aspects of this highly dynamic research field and cover topics from applied mathematics, physics and engineering.
Third International Symposium On Domain Decomposition Methods For Partial Differential Equations
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Author : Tony F. Chan
language : en
Publisher: SIAM
Release Date : 1990-01-01
Third International Symposium On Domain Decomposition Methods For Partial Differential Equations written by Tony F. Chan and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-01 with Mathematics categories.