Elliptic Hyperbolic Partial Differential Equations

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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.

Applied Partial Differential Equations An Introduction

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Author : Alan Jeffrey
language : en
Publisher: Academic Press
Release Date : 2003

Applied Partial Differential Equations An Introduction written by Alan Jeffrey and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

This work is for students who need more than the purely numerical solutions provided by programs like the MATLAB PDE Toolbox, and those obtained by the method of separation of variables.

Elliptic Hyperbolic Partial Differential Equations

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Author : Thomas H. Otway
language : en
Publisher:
Release Date : 2015

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

Elements Of Partial Differential Equations

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Author : Pavel Drábek
language : en
Publisher: Walter de Gruyter
Release Date : 2008-07-16

Elements Of Partial Differential Equations written by Pavel Drábek and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-16 with Mathematics categories.

This textbook presents a first introduction to PDEs on an elementary level, enabling the reader to understand what partial differential equations are, where they come from and how they can be solved. The intention is that the reader understands the basic principles which are valid for particular types of PDEs, and to acquire some classical methods to solve them, thus the authors restrict their considerations to fundamental types of equations and basic methods. Only basic facts from calculus and linear ordinary differential equations of first and second order are needed as a prerequisite. An elementary introduction to the basic principles of partial differential equations. With many illustrations. The book is addressed to students who intend to specialize in mathematics as well as to students of physics, engineering, and economics.

Elliptic Hyperbolic And Mixed Complex Equations With Parabolic Degeneracy Including Tricomi Bers And Tricomi Frankl Rassias Problems

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Author : Guo Chun Wen
language : en
Publisher: World Scientific
Release Date : 2007-12-13

Elliptic Hyperbolic And Mixed Complex Equations With Parabolic Degeneracy Including Tricomi Bers And Tricomi Frankl Rassias Problems written by Guo Chun Wen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-13 with Mathematics categories.

In the recent half-century, many mathematicians have investigated various problems on several equations of mixed type and obtained interesting results, with important applications to gas dynamics. However, the Tricomi problem of general mixed type equations of second order with parabolic degeneracy has not been completely solved, particularly the Tricomi and Frankl problems for general Chaplygin equation in multiply connected domains posed by L Bers, and the existence, regularity of solutions of the above problems for mixed equations with non-smooth degenerate curve in several domains posed by J M Rassias.The method revealed in this book is unlike any other, in which the hyperbolic number and hyperbolic complex function in hyperbolic domains, and the complex number and complex function in elliptic domains are used. The corresponding problems for first order complex equations with singular coefficients are first discussed, and then the problems for second order complex equations are considered, where we pose the new partial derivative notations and complex analytic methods such that the forms of the above first order complex equations in hyperbolic and elliptic domains are wholly identical. In the meantime, the estimates of solutions for the above problems are obtained, hence many open problems including the above Tricomi- Bers and Tricomi-Frankl-Rassias problems can be solved.

Partial Differential Equations

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Author : Phoolan Prasad
language : en
Publisher: New Age International
Release Date : 1985

Partial Differential Equations written by Phoolan Prasad and has been published by New Age International this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Differential equations, Partial categories.

This book provides a basic introductory course in partial differential equations, in which theory and applications are interrelated and developed side by side. Emphasis is on proofs, which are not only mathematically rigorous, but also constructive, where the structure and properties of the solution are investigated in detail. The authors feel that it is no longer necessary to follow the tradition of introducing the subject by deriving various partial differential equations of continuum mechanics and theoretical physics. Therefore, the subject has been introduced by mathematical analysis of the simplest, yet one of the most useful (from the point of view of applications), class of partial differential equations, namely the equations of first order, for which existence, uniqueness and stability of the solution of the relevant problem (Cauchy problem) is easy to discuss. Throughout the book, attempt has been made to introduce the important ideas from relatively simple cases, some times by referring to physical processes, and then extending them to more general systems.

Encyclopaedia Of Mathematics

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Author : Michiel Hazewinkel
language : en
Publisher: Springer
Release Date : 2013-12-20

Encyclopaedia Of Mathematics written by Michiel Hazewinkel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-20 with Mathematics categories.

Partial Differential Equation And Mechanics

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Author : Mr. Rohit Manglik
language : en
Publisher: EduGorilla Publication
Release Date : 2024-03-18

Partial Differential Equation And Mechanics written by Mr. Rohit Manglik and has been published by EduGorilla Publication this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-18 with Mathematics categories.

EduGorilla Publication is a trusted name in the education sector, committed to empowering learners with high-quality study materials and resources. Specializing in competitive exams and academic support, EduGorilla provides comprehensive and well-structured content tailored to meet the needs of students across various streams and levels.

Hamiltonian Partial Differential Equations And Applications

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Author : Philippe Guyenne
language : en
Publisher: Springer
Release Date : 2015-09-11

Hamiltonian Partial Differential Equations And Applications written by Philippe Guyenne and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-11 with Mathematics categories.

This book is a unique selection of work by world-class experts exploring the latest developments in Hamiltonian partial differential equations and their applications. Topics covered within are representative of the field’s wide scope, including KAM and normal form theories, perturbation and variational methods, integrable systems, stability of nonlinear solutions as well as applications to cosmology, fluid mechanics and water waves. The volume contains both surveys and original research papers and gives a concise overview of the above topics, with results ranging from mathematical modeling to rigorous analysis and numerical simulation. It will be of particular interest to graduate students as well as researchers in mathematics and physics, who wish to learn more about the powerful and elegant analytical techniques for Hamiltonian partial differential equations.

Partial Differential Equations In Physics

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Author :
language : en
Publisher: Academic Press
Release Date : 1949-01-01

Partial Differential Equations In Physics written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1949-01-01 with Mathematics categories.

The topic with which I regularly conclude my six-term series of lectures in Munich is the partial differential equations of physics. We do not really deal with mathematical physics, but with physical mathematics; not with the mathematical formulation of physical facts, but with the physical motivation of mathematical methods. The oftmentioned "prestabilized harmony between what is mathematically interesting and what is physically important is met at each step and lends an esthetic - I should like to say metaphysical -- attraction to our subject. The problems to be treated belong mainly to the classical matherhatical literature, as shown by their connection with the names of Laplace, Fourier, Green, Gauss, Riemann, and William Thomson. In order to show that these methods are adequate to deal with actual problems, we treat the propagation of radio waves in some detail in Chapter VI.