Multiplicative Partial Differential Equations
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Multiplicative Partial Differential Equations
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Author : Svetlin G. Georgiev
language : en
Publisher: CRC Press
Release Date : 2023-10-30
Multiplicative Partial Differential Equations written by Svetlin G. Georgiev and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-30 with Mathematics categories.
Multiplicative Partial Differential Equations presents an introduction to the theory of multiplicative partial differential equations (MPDEs). It is suitable for all types of basic courses on MPDEs. The authors' aim is to present a clear and well-organized treatment of the concepts behind the development of mathematics and solution techniques. The text is presented in a highly readable, mathematically solid format. Many practical problems are illustrated, displaying a wide variety of solution techniques. Features Includes new classification and canonical forms of second-order MPDEs Proposes the latest techniques in solving the multiplicative wave equation such as the method of separation of variables and the energy method Useful in allowing for the basic properties of multiplicative elliptic problems, fundamental solutions, multiplicative integral representation of multiplicative harmonic functions, meant-value formulas, strong principle of maximum, multiplicative Poisson equation, multiplicative Green functions, method of separation of variables, and theorems of Liouville and Harnack
Controllability Of Partial Differential Equations Governed By Multiplicative Controls
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Author : Alexander Y. Khapalov
language : en
Publisher: Springer
Release Date : 2010-05-19
Controllability Of Partial Differential Equations Governed By Multiplicative Controls written by Alexander Y. Khapalov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-19 with Mathematics categories.
This monograph addresses the global controllability of partial differential equations in the context of multiplicative (or bilinear) controls, which enter the model equations as coefficients. The methodology is illustrated with a variety of model equations.
Partial Differential Equations And Group Theory
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Author : J.F. Pommaret
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Partial Differential Equations And Group Theory written by J.F. Pommaret 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 2013-03-09 with Mathematics categories.
Ordinary differential control thPory (the classical theory) studies input/output re lations defined by systems of ordinary differential equations (ODE). The various con cepts that can be introduced (controllability, observability, invertibility, etc. ) must be tested on formal objects (matrices, vector fields, etc. ) by means of formal operations (multiplication, bracket, rank, etc. ), but without appealing to the explicit integration (search for trajectories, etc. ) of the given ODE. Many partial results have been re cently unified by means of new formal methods coming from differential geometry and differential algebra. However, certain problems (invariance, equivalence, linearization, etc. ) naturally lead to systems of partial differential equations (PDE). More generally, partial differential control theory studies input/output relations defined by systems of PDE (mechanics, thermodynamics, hydrodynamics, plasma physics, robotics, etc. ). One of the aims of this book is to extend the preceding con cepts to this new situation, where, of course, functional analysis and/or a dynamical system approach cannot be used. A link will be exhibited between this domain of applied mathematics and the famous 'Backlund problem', existing in the study of solitary waves or solitons. In particular, we shall show how the methods of differ ential elimination presented here will allow us to determine compatibility conditions on input and/or output as a better understanding of the foundations of control the ory. At the same time we shall unify differential geometry and differential algebra in a new framework, called differential algebraic geometry.
Multiplication Of Distributions And Applications To Partial Differential Equations
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Author : Michael Oberguggenberger
language : en
Publisher:
Release Date : 1992
Multiplication Of Distributions And Applications To Partial Differential Equations written by Michael Oberguggenberger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Differential equations, Hyperbolic categories.
Multiplicative Analytic Geometry
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Author : Svetlin G. Georgiev
language : en
Publisher: CRC Press
Release Date : 2022-11-24
Multiplicative Analytic Geometry written by Svetlin G. Georgiev and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-24 with Mathematics categories.
This book is devoted to multiplicative analytic geometry. The book reflects recent investigations into the topic. The reader can use the main formulae for investigations of multiplicative differential equations, multiplicative integral equations and multiplicative geometry. The authors summarize the most recent contributions in this area. The goal of the authors is to bring the most recent research on the topic to capable senior undergraduate students, beginning graduate students of engineering and science and researchers in a form to advance further study. The book contains eight chapters. The chapters in the book are pedagogically organized. Each chapter concludes with a section with practical problems. Two operations, differentiation and integration, are basic in calculus and analysis. In fact, they are the infinitesimal versions of the subtraction and addition operations on numbers, respectively. In the period from 1967 till 1970, Michael Grossman and Robert Katz gave definitions of a new kind of derivative and integral, moving the roles of subtraction and addition to division and multiplication, and thus established a new calculus, called multiplicative calculus. Multiplicative calculus can especially be useful as a mathematical tool for economics and finance. Multiplicative Analytic Geometry builds upon multiplicative calculus and advances the theory to the topics of analytic and differential geometry.
Partial Differential Equations I
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Author : Michael E. Taylor
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-29
Partial Differential Equations I written by Michael E. Taylor 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 2010-10-29 with Mathematics categories.
The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces. These tools are then applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations.The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis.
Multiplicative Differential Equations
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Author : Svetlin Georgiev
language : en
Publisher: CRC Press
Release Date : 2023-06-30
Multiplicative Differential Equations written by Svetlin Georgiev and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-30 with Mathematics categories.
Multiplicative Differential Equations: Volume II is the second part of a comprehensive approach to the subject. It continues a series of books written by the authors on multiplicative, geometric approaches to key mathematical topics. This volume is devoted to the theory of multiplicative differential systems. The asymptotic behavior of the solutions of such systems is studied. Stability theory for multiplicative linear and nonlinear systems is introduced and boundary value problems for second-order multiplicative linear and nonlinear equations are explored. The authors also present first-order multiplicative partial differential equations. Each chapter ends with a section of practical problems. The text is accessible to graduate students and researchers in mathematics, physics, engineering and biology.
Geometric Level Set Methods In Imaging Vision And Graphics
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Author : Stanley Osher
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-07-17
Geometric Level Set Methods In Imaging Vision And Graphics written by Stanley Osher 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 2003-07-17 with Computers categories.
Here is, for the first time, a book that clearly explains and applies new level set methods to problems and applications in computer vision, graphics, and imaging. It is an essential compilation of survey chapters from the leading researchers in the field. The applications of the methods are emphasized.
Delay Ordinary And Partial Differential Equations
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Author : Andrei D. Polyanin
language : en
Publisher: CRC Press
Release Date : 2023-08-28
Delay Ordinary And Partial Differential Equations written by Andrei D. Polyanin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-28 with Mathematics categories.
Delay Ordinary and Partial Differential Equations is devoted to linear and nonlinear ordinary and partial differential equations with constant and variable delay. It considers qualitative features of delay differential equations and formulates typical problem statements. Exact, approximate analytical and numerical methods for solving such equations are described, including the method of steps, methods of integral transformations, method of regular expansion in a small parameter, method of matched asymptotic expansions, iteration-type methods, Adomian decomposition method, collocation method, Galerkin-type projection methods, Euler and Runge-Kutta methods, shooting method, method of lines, finite-difference methods for PDEs, methods of generalized and functional separation of variables, method of functional constraints, method of generating equations, and more. The presentation of the theoretical material is accompanied by examples of the practical application of methods to obtain the desired solutions. Exact solutions are constructed for many nonlinear delay reaction-diffusion and wave-type PDEs that depend on one or more arbitrary functions. A review is given of the most common mathematical models with delay used in population theory, biology, medicine, economics, and other applications. The book contains much new material previously unpublished in monographs. It is intended for a broad audience of scientists, university professors, and graduate and postgraduate students specializing in applied and computational mathematics, mathematical physics, mechanics, control theory, biology, medicine, chemical technology, ecology, economics, and other disciplines. Individual sections of the book and examples are suitable for lecture courses on applied mathematics, mathematical physics, and differential equations for delivering special courses and for practical training.
Handbook Of Nonlinear Partial Differential Equations
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Author : Andrei D. Polyanin
language : en
Publisher: CRC Press
Release Date : 2004-06-02
Handbook Of Nonlinear Partial Differential Equations written by Andrei D. Polyanin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-02 with Mathematics categories.
The Handbook of Nonlinear Partial Differential Equations is the latest in a series of acclaimed handbooks by these authors and presents exact solutions of more than 1600 nonlinear equations encountered in science and engineering--many more than any other book available. The equations include those of parabolic, hyperbolic, elliptic and other types, and the authors pay special attention to equations of general form that involve arbitrary functions. A supplement at the end of the book discusses the classical and new methods for constructing exact solutions to nonlinear equations. To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the equations in increasing order of complexity. Highlights of the Handbook: