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 The authors offer material previously unpublished in book form, including treatments of the life span of classical solutions, the construction of singularities of generalized solutions, new existence and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).
Handbook Of Exact Solutions To Mathematical Equations
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Author : Andrei D. Polyanin
language : en
Publisher: CRC Press
Release Date : 2024-08-26
Handbook Of Exact Solutions To Mathematical 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 2024-08-26 with Mathematics categories.
This reference book describes the exact solutions of the following types of mathematical equations: ● Algebraic and Transcendental Equations ● Ordinary Differential Equations ● Systems of Ordinary Differential Equations ● First-Order Partial Differential Equations ● Linear Equations and Problems of Mathematical Physics ● Nonlinear Equations of Mathematical Physics ● Systems of Partial Differential Equations ● Integral Equations ● Difference and Functional Equations ● Ordinary Functional Differential Equations ● Partial Functional Differential Equations The book delves into equations that find practical applications in a wide array of natural and engineering sciences, including the theory of heat and mass transfer, wave theory, hydrodynamics, gas dynamics, combustion theory, elasticity theory, general mechanics, theoretical physics, nonlinear optics, biology, chemical engineering sciences, ecology, and more. Most of these equations are of a reasonably general form and dependent on free parameters or arbitrary functions. The Handbook of Exact Solutions to Mathematical Equations generally has no analogs in world literature and contains a vast amount of new material. The exact solutions given in the book, being rigorous mathematical standards, can be used as test problems to assess the accuracy and verify the adequacy of various numerical and approximate analytical methods for solving mathematical equations, as well as to check and compare the effectiveness of exact analytical methods.
Nonlinear Partial Differential Equations For Scientists And Engineers
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Author : Lokenath Debnath
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
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 2013-11-11 with Mathematics categories.
"An exceptionally complete overview. There are numerous examples and the emphasis is on applications to almost all areas of science and engineering. There is truly something for everyone here. This reviewer feels that it is a very hard act to follow, and recommends it strongly. [This book] is a jewel." - Applied Mechanics Review (Review of First Edition) This expanded and revised second edition is a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied applications. Building upon the successful material of the first book, this edition contains updated modern examples and applications from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation. Methods and properties of solutions are presented, along with their physical significance, making the book more useful for a diverse readership.
Acta Mathematica Vietnamica
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Author :
language : en
Publisher:
Release Date : 2005
Acta Mathematica Vietnamica written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Abstract And Applied Analysis Proceedings Of The International Conference
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Author : Nguyen Minh Chuong
language : en
Publisher: World Scientific
Release Date : 2004-06-01
Abstract And Applied Analysis Proceedings Of The International Conference written by Nguyen Minh Chuong and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-01 with Mathematics categories.
This volume takes up various topics in Mathematical Analysis including boundary and initial value problems for Partial Differential Equations and Functional Analytic methods.Topics include linear elliptic systems for composite material — the coefficients may jump from domain to domain; Stochastic Analysis — many applied problems involve evolution equations with random terms, leading to the use of stochastic analysis.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences
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.
Partial Differential Equations
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Author : Mr. Rohit Manglik
language : en
Publisher: EduGorilla Publication
Release Date : 2024-07-23
Partial Differential Equations 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 2024-07-23 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.
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: