The Characteristic Method And Its Generalizations For First Order Nonlinear Partial Differential Equations
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The Characteristic Method And Its Generalizations For First Order Nonlinear Partial Differential Equations
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Author : Tran Duc Van
language : en
Publisher: CRC Press
Release Date : 1999-06-25
The Characteristic Method And Its Generalizations For First Order Nonlinear Partial Differential Equations written by Tran Duc Van and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-06-25 with Mathematics categories.
Despite decades of research and progress in the theory of generalized solutions to first-order nonlinear partial differential equations, a gap between the local and the global theories remains: The Cauchy characteristic method yields the local theory of classical solutions. Historically, the global theory has principally depended on the vanishing viscosity method. The authors of this volume help bridge the gap between the local and global theories by using the characteristic method as a basis for setting a theoretical framework for the study of global generalized solutions. That is, they extend the smooth solutions obtained by the characteristic method. The authors offer material previously unpublished in book form, including treatments of the life span of classical solutions, the construction of singularities of generalized solutions, new existence and uniqueness theorems on minimax solutions, differential inequalities of Haar type and their application to the uniqueness of global, semi-classical solutions, and Hopf-type explicit formulas for global solutions. These subjects yield interesting relations between purely mathematical theory and the applications of first-order nonlinear PDEs. The Characteristic Method and Its Generalizations for First-Order Nonlinear Partial Differential Equations represents a comprehensive exposition of the authors' works over the last decade. The book is self-contained and assumes only basic measure theory, topology, and ordinary differential equations as prerequisites. With its innovative approach, new results, and many applications, it will prove valuable to mathematicians, physicists, and engineers and especially interesting to researchers in nonlinear PDEs, differential inequalities, multivalued analysis, differential games, and related topics in applied analysis.
Characteristic Method And Its Generalizations For First Order Nonlinear Pde
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Author : Duc Van Tran
language : en
Publisher:
Release Date : 1999-01
Characteristic Method And Its Generalizations For First Order Nonlinear Pde written by Duc Van Tran and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01 with categories.
The Characteristic Method and Its Generalizations for First-Order Nonl inear Partial Differential Equations represents a comprehensive exposi tion of the authors' works over the last decade. The book is self-cont ained and assumes only basic measure theory, topology, and ordinary di fferential equations as prerequisites. With its innovative approach, n ew results, and many applications, it will prove valuable to mathemati cians, physicists, and engineers and especially interesting to researc hers in nonlinear PDEs, differential inequalities, multivalued analysi s, differential games, and related topics in applied analysis.
Solving Nonlinear Partial Differential Equations With Maple And Mathematica
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Author : Inna Shingareva
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-07-24
Solving Nonlinear Partial Differential Equations With Maple And Mathematica written by Inna Shingareva 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 2011-07-24 with Mathematics categories.
The emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple and Mathematica, facilitates a deeper understanding of the subject. Among a big number of CAS, we choose the two systems, Maple and Mathematica, that are used worldwide by students, research mathematicians, scientists, and engineers. As in the our previous books, we propose the idea to use in parallel both systems, Maple and Mathematica, since in many research problems frequently it is required to compare independent results obtained by using different computer algebra systems, Maple and/or Mathematica, at all stages of the solution process. One of the main points (related to CAS) is based on the implementation of a whole solution method (e.g. starting from an analytical derivation of exact governing equations, constructing discretizations and analytical formulas of a numerical method, performing numerical procedure, obtaining various visualizations, and comparing the numerical solution obtained with other types of solutions considered in the book, e.g. with asymptotic solution).
Nonlinear Partial Differential Equations For Scientists And Engineers
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Author : Lokenath Debnath
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-02-20
Nonlinear Partial Differential Equations For Scientists And Engineers written by Lokenath Debnath 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 2010-02-20 with Mathematics categories.
This expanded, revised edition is a thorough and systematic treatment of linear and nonlinear partial differential equations and their varied applications. It contains updated modern examples and applications from diverse fields. Methods and properties of solutions, along with their physical significance, make the book useful for a diverse readership including graduates, researchers, and professionals in mathematics, physics and engineering.
Using The Mathematics Literature
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Author : Kristine K. Fowler
language : en
Publisher: CRC Press
Release Date : 2004-05-25
Using The Mathematics Literature written by Kristine K. Fowler and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-05-25 with Language Arts & Disciplines categories.
This reference serves as a reader-friendly guide to every basic tool and skill required in the mathematical library and helps mathematicians find resources in any format in the mathematics literature. It lists a wide range of standard texts, journals, review articles, newsgroups, and Internet and database tools for every major subfield in mathematics and details methods of access to primary literature sources of new research, applications, results, and techniques. Using the Mathematics Literature is the most comprehensive and up-to-date resource on mathematics literature in both print and electronic formats, presenting time-saving strategies for retrieval of the latest information.
Handbook Of Mathematics For Engineers And Scientists
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Author : Andrei D. Polyanin
language : en
Publisher: CRC Press
Release Date : 2006-11-27
Handbook Of Mathematics For Engineers And Scientists 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 2006-11-27 with Mathematics categories.
Covering the main fields of mathematics, this handbook focuses on the methods used for obtaining solutions of various classes of mathematical equations that underlie the mathematical modeling of numerous phenomena and processes in science and technology. The authors describe formulas, methods, equations, and solutions that are frequently used in scientific and engineering applications and present classical as well as newer solution methods for various mathematical equations. The book supplies numerous examples, graphs, figures, and diagrams and contains many results in tabular form, including finite sums and series and exact solutions of differential, integral, and functional equations.
Thermo Mechanics Applications And Engineering Technology
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Author : Zied Driss
language : en
Publisher: Springer
Release Date : 2018-01-30
Thermo Mechanics Applications And Engineering Technology written by Zied Driss and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-30 with Technology & Engineering categories.
This book focuses on the dissemination of information of permanent interest in thermo-mechanics applications and engineering technology. Contributions have clear relevance to industrial device and a relatively straightforward or feasible path to application. Chapters are sought that have long-term relevance to specific applications including convective heat transfer, fluid mechanics, combustion, aerodynamics, hydrodynamics, turbomachinery and multi-phase flows. In fact, many aspects in industrial operations and daily life are closely related to thermo-mechanics processes. Along with the development of computer industry and the advancement of numerical methods, solid foundation in both hardware and software has been established to study the processes by using numerical simulation methods, which play important roles in the ways of extending research topics, reducing research costs, discovering new phenomena, and developing new technologies. The presented case studies and development approaches aim to provide the readers, such as engineers and PhD students, with basic and applied studies broadly related to the Thermo-Mechanics Applications and Engineering Technology.
Nonlinear Partial Differential Equations
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Author : W. F. Ames
language : en
Publisher: Academic Press
Release Date : 2014-05-12
Nonlinear Partial Differential Equations written by W. F. Ames and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Mathematics categories.
Nonlinear Partial Differential Equations: A Symposium on Methods of Solution is a collection of papers presented at the seminar on methods of solution for nonlinear partial differential equations, held at the University of Delaware, Newark, Delaware on December 27-29, 1965. The sessions are divided into four Symposia: Analytic Methods, Approximate Methods, Numerical Methods, and Applications. Separating 19 lectures into chapters, this book starts with a presentation of the methods of similarity analysis, particularly considering the merits, advantages and disadvantages of the methods. The subsequent chapters describe the fundamental ideas behind the methods for the solution of partial differential equation derived from the theory of dynamic programming and from finite systems of ordinary differential equations. These topics are followed by reviews of the principles to the lubrication approximation and compressible boundary-layer flow computation. The discussion then shifts to several applications of nonlinear partial differential equations, including in electrical problems, two-phase flow, hydrodynamics, and heat transfer. The remaining chapters cover other solution methods for partial differential equations, such as the synergetic approach. This book will prove useful to applied mathematicians, physicists, and engineers.
Functional Analytic And Complex Methods Their Interactions And Applications To Partial Differential Equations
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Author : Helmut Florian
language : en
Publisher: World Scientific
Release Date : 2001
Functional Analytic And Complex Methods Their Interactions And Applications To Partial Differential Equations written by Helmut Florian and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
Functional analysis is not only a tool for unifying mathematical analysis, but it also provides the background for today''s rapid development of the theory of partial differential equations. Using concepts of functional analysis, the field of complex analysis has developed methods (such as the theory of generalized analytic functions) for solving very general classes of partial differential equations. This book is aimed at promoting further interactions of functional analysis, partial differential equations, and complex analysis including its generalizations such as Clifford analysis. New interesting problems in the field of partial differential equations concern, for instance, the Dirichlet problem for hyperbolic equations. Applications to mathematical physics address mainly Maxwell''s equations, crystal optics, dynamical problems for cusped bars, and conservation laws. Sample Chapter(s). Hyperbolic Equations, Waves and the Singularity Theory (858 KB). Contents: Boundary Value Problems and Initial Value Problems for Partial Differential Equations; Applications of Functional-Analytic and Complex Methods to Mathematical Physics; Partial Complex Differential Equations in the Plane; Complex Methods in Higher Dimensions. Readership: Researchers, lecturers and graduate students in the fields of analysis & differential equations, applied mathematics and mathematical physics.
Functional Analytic And Complex Methods Their Interactions And Applications To Partial Differential Equations Proceedings Of The International Graz Workshop
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Author : Helmut Florian
language : en
Publisher: World Scientific
Release Date : 2001-11-12
Functional Analytic And Complex Methods Their Interactions And Applications To Partial Differential Equations Proceedings Of The International Graz Workshop written by Helmut Florian and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-11-12 with Mathematics categories.
Functional analysis is not only a tool for unifying mathematical analysis, but it also provides the background for today's rapid development of the theory of partial differential equations. Using concepts of functional analysis, the field of complex analysis has developed methods (such as the theory of generalized analytic functions) for solving very general classes of partial differential equations.This book is aimed at promoting further interactions of functional analysis, partial differential equations, and complex analysis including its generalizations such as Clifford analysis. New interesting problems in the field of partial differential equations concern, for instance, the Dirichlet problem for hyperbolic equations. Applications to mathematical physics address mainly Maxwell's equations, crystal optics, dynamical problems for cusped bars, and conservation laws. remove /a remove