The Dirichlet Problem For Elliptic Hyperbolic Equations Of Keldysh Type

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The Dirichlet Problem For Elliptic Hyperbolic Equations Of Keldysh Type

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Author : Thomas H. Otway
language : en
Publisher: Springer
Release Date : 2012-01-06

The Dirichlet Problem For Elliptic Hyperbolic Equations Of Keldysh Type written by Thomas H. Otway and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-06 with Mathematics categories.

Partial differential equations of mixed elliptic-hyperbolic type arise in diverse areas of physics and geometry, including fluid and plasma dynamics, optics, cosmology, traffic engineering, projective geometry, geometric variational theory, and the theory of isometric embeddings. And yet even the linear theory of these equations is at a very early stage. This text examines various Dirichlet problems which can be formulated for equations of Keldysh type, one of the two main classes of linear elliptic-hyperbolic equations. Open boundary conditions (in which data are prescribed on only part of the boundary) and closed boundary conditions (in which data are prescribed on the entire boundary) are both considered. Emphasis is on the formulation of boundary conditions for which solutions can be shown to exist in an appropriate function space. Specific applications to plasma physics, optics, and analysis on projective spaces are discussed. (From the preface)

The Dirichlet Problem For Elliptic Hyperbolic Equations Of Keldysh Type

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Author : Thomas H. Otway
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-07

The Dirichlet Problem For Elliptic Hyperbolic Equations Of Keldysh Type written by Thomas H. Otway 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 2012-01-07 with Mathematics categories.

Partial differential equations of mixed elliptic-hyperbolic type arise in diverse areas of physics and geometry, including fluid and plasma dynamics, optics, cosmology, traffic engineering, projective geometry, geometric variational theory, and the theory of isometric embeddings. And yet even the linear theory of these equations is at a very early stage. This text examines various Dirichlet problems which can be formulated for equations of Keldysh type, one of the two main classes of linear elliptic-hyperbolic equations. Open boundary conditions (in which data are prescribed on only part of the boundary) and closed boundary conditions (in which data are prescribed on the entire boundary) are both considered. Emphasis is on the formulation of boundary conditions for which solutions can be shown to exist in an appropriate function space. Specific applications to plasma physics, optics, and analysis on projective spaces are discussed. (From the preface)

Elliptic Hyperbolic Partial Differential Equations

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Author : Thomas H. Otway
language : en
Publisher: Springer
Release Date : 2015-07-08

Elliptic Hyperbolic Partial Differential Equations written by Thomas H. Otway and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-08 with Mathematics categories.

This text is a concise introduction to the partial differential equations which change from elliptic to hyperbolic type across a smooth hypersurface of their domain. These are becoming increasingly important in diverse sub-fields of both applied mathematics and engineering, for example: • The heating of fusion plasmas by electromagnetic waves • The behaviour of light near a caustic • Extremal surfaces in the space of special relativity • The formation of rapids; transonic and multiphase fluid flow • The dynamics of certain models for elastic structures • The shape of industrial surfaces such as windshields and airfoils • Pathologies of traffic flow • Harmonic fields in extended projective space They also arise in models for the early universe, for cosmic acceleration, and for possible violation of causality in the interiors of certain compact stars. Within the past 25 years, they have become central to the isometric embedding of Riemannian manifolds and the prescription of Gauss curvature for surfaces: topics in pure mathematics which themselves have important applications. Elliptic−Hyperbolic Partial Differential Equations is derived from a mini-course given at the ICMS Workshop on Differential Geometry and Continuum Mechanics held in Edinburgh, Scotland in June 2013. The focus on geometry in that meeting is reflected in these notes, along with the focus on quasilinear equations. In the spirit of the ICMS workshop, this course is addressed both to applied mathematicians and to mathematically-oriented engineers. The emphasis is on very recent applications and methods, the majority of which have not previously appeared in book form.

Lipman Bers A Life In Mathematics

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Author : Linda Keen
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-09-15

Lipman Bers A Life In Mathematics written by Linda Keen 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 2015-09-15 with Biography & Autobiography categories.

The book is part biography and part collection of mathematical essays that gives the reader a perspective on the evolution of an interesting mathematical life. It is all about Lipman Bers, a giant in the mathematical world who lived in turbulent and exciting times. It captures the essence of his mathematics, a development and transition from applied mathematics to complex analysis--quasiconformal mappings and moduli of Riemann surfaces--and the essence of his personality, a progression from a young revolutionary refugee to an elder statesman in the world of mathematics and a fighter for global human rights and the end of political torture. The book contains autobiographical material and short reprints of his work. The main content is in the exposition of his research contributions, sometimes with novel points of view, by students, grand-students, and colleagues. The research described was fundamental to the growth of a central part of 20th century mathematics that, now in the 21st century, is in a healthy state with much current interest and activity. The addition of personal recollections, professional tributes, and photographs yields a picture of a man, his personal and professional family, and his time.

Digital Humanities In Practice

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Author : Claire Warwick
language : en
Publisher: Facet Publishing
Release Date : 2012-10-09

Digital Humanities In Practice written by Claire Warwick and has been published by Facet Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-09 with Language Arts & Disciplines categories.

This cutting-edge and comprehensive introduction to digital humanities explains the scope of the discipline and state of the art and provides a wide-ranging insight into emerging topics and avenues of research. Each chapter interweaves the expert commentary of leading academics with analysis of current research and practice, exploring the possibilities and challenges that occur when culture and digital technologies intersect. International case studies of projects ranging from crowdsourced manuscript transcription to computational reconstruction of frescoes are included in each chapter, providing a wealth of information and inspiration. QR codes within each chapter link to a dedicated website where additional content, such as further case studies, is located. Key topics covered include: • studying users and readers • social media and crowdsourcing • digitization and digital resources • image processing in the digital humanities • 3D recording and museums • electronic text and text encoding • book history, texts and digital editing • open access and online teaching of digital humanities • institutional models for digital humanities. Readership: This is an essential practical guide for academics, researchers, librarians and professionals involved in the digital humanities. It will also be core reading for all humanities students and those taking courses in the digital humanities in particular.

The Mathematics Of Shock Reflection Diffraction And Von Neumann S Conjectures

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Author : Gui-Qiang G Chen
language : en
Publisher: Princeton University Press
Release Date : 2018-02-27

The Mathematics Of Shock Reflection Diffraction And Von Neumann S Conjectures written by Gui-Qiang G Chen and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-27 with Mathematics categories.

This book offers a survey of recent developments in the analysis of shock reflection-diffraction, a detailed presentation of original mathematical proofs of von Neumann's conjectures for potential flow, and a collection of related results and new techniques in the analysis of partial differential equations (PDEs), as well as a set of fundamental open problems for further development. Shock waves are fundamental in nature. They are governed by the Euler equations or their variants, generally in the form of nonlinear conservation laws—PDEs of divergence form. When a shock hits an obstacle, shock reflection-diffraction configurations take shape. To understand the fundamental issues involved, such as the structure and transition criteria of different configuration patterns, it is essential to establish the global existence, regularity, and structural stability of shock reflection-diffraction solutions. This involves dealing with several core difficulties in the analysis of nonlinear PDEs—mixed type, free boundaries, and corner singularities—that also arise in fundamental problems in diverse areas such as continuum mechanics, differential geometry, mathematical physics, and materials science. Presenting recently developed approaches and techniques, which will be useful for solving problems with similar difficulties, this book opens up new research opportunities.

Equations Of The Mixed Type

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Author : A. V. Bitsadze
language : en
Publisher: Elsevier
Release Date : 2014-05-16

Equations Of The Mixed Type written by A. V. Bitsadze and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-16 with Mathematics categories.

Equations of the Mixed Type compiles a series of lectures on certain fundamental questions in the theory of equations of mixed type. This book investigates the series of problems concerning linear partial differential equations of the second order in two variables, and possessing the property that the type of the equation changes either on the boundary of or inside the considered domain. Topics covered include general remarks on linear partial differential equations of mixed type; study of the solutions of second order hyperbolic equations with initial conditions given along the lines of parabolicity; and study of the solutions of second order elliptic equations for a domain, the boundary of which includes a segment of the curve of parabolic degeneracy. The problem of Tricomi and other mixed problems are also deliberated in this text. This publication is a good reference for students and researchers conducting work on the theory of equations of mixed type.

Analysis And Applied Mathematics

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Author : Allaberen Ashyralyev
language : en
Publisher: Springer Nature
Release Date : 2024-08-27

Analysis And Applied Mathematics written by Allaberen Ashyralyev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-27 with Mathematics categories.

This book presents extended abstracts of the Analysis and Applied Mathematics seminar organized jointly by Bahçeşehir University, Istanbul, Turkey, Ghent Analysis & PDE Center, Ghent University, Ghent, Belgium and the Institute Mathematics & Math. Modeling, Almaty, Kazakhstan. The book is of value to professional mathematicians as well as advanced students in the fields of analysis and applied mathematics. The goal of the seminar is to provide a forum for researchers and scientists from different regions to communicate their recent developments and to present their original results in various fields of analysis and applied mathematics. All of the articles contain new results and are peer-reviewed. The volume reflects the latest developments in the area of analysis and applied mathematics and their interdisciplinary applications.

Nonclassical Thermoelastic Problems In Nonlinear Dynamics Of Shells

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Author : Jan Awrejcewicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Nonclassical Thermoelastic Problems In Nonlinear Dynamics Of Shells written by Jan Awrejcewicz 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 2012-12-06 with Technology & Engineering categories.

This monograph describes some approaches to the nonlinear theory of plates and shells. By nonclassical approaches we mean the desciption of problems with mathematical models of different sizes (two-and three-dimensional dif ferential equations) and different types (differential equations of hyperbolic and parabolic type in the spatial coordinates). The nonlinearities investigated are also of various categories: geometrical, physical, elasto-plastic, and peri odic. Creating such types of mathematical models and their detailed justifica tion allows us to achieve the most accurate description of the real behaviour of shell-type structures. These models allow us to include interaction between the strain and temperature fields and coupling between the displacement field and the external influence of a transonic gas flow. The mathematical treatment of such models helps us greatly in obtaining reliable results by numerical computation. It appears that the most dangerous situation for thin shallow shells is the conjunction of a static load with dynamic interactions. Such combined loads very often cause buckling of shell structures, and in many cases a series of bucklings, which can cause fracture. The failure of a structure usually needs a small amount of time. Therefore the lifetime of a shell structure depends strongly on nonelastic deflections and it is important to mathematically model shell structures as precisely as possible. This monograph is one of several devoted to this subject. Now we shall briefly describe the contents of the book. Note that not all of the results presented here have been published in textbook format.

Encyclopaedia Of Mathematics

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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01

Encyclopaedia Of Mathematics written by Michiel Hazewinkel 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 2013-12-01 with Mathematics categories.

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.