Elliptic Hyperbolic And Mixed Complex Equations With Parabolic Degeneracy
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Elliptic Hyperbolic And Mixed Complex Equations With Parabolic Degeneracy
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Author : Guo Chun Wen
language : en
Publisher: World Scientific
Release Date : 2008
Elliptic Hyperbolic And Mixed Complex Equations With Parabolic Degeneracy 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 2008 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 TricomiOCo Bers and TricomiOCoFranklOCoRassias problems can be solved. Sample Chapter(s). Chapter 1: Elliptic Complex Equations of First Order (247 KB). Contents: Elliptic Complex Equations of First Order; Elliptic Complex Equations of Second Order; Hyperbolic Complex Equations of First and Second Orders; First Order Complex Equations of Mixed Type; Second Order Linear Equations of Mixed Type; Second Order Quasilinear Equations of Mixed Type. Readership: Graduate students and academics in analysis, differential equations and applied mathematics.
Linear And Quasilinear Complex Equations Of Hyperbolic And Mixed Types
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Author : Guo Chun Wen
language : en
Publisher: CRC Press
Release Date : 2002-08-22
Linear And Quasilinear Complex Equations Of Hyperbolic And Mixed Types written by Guo Chun Wen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-08-22 with Mathematics categories.
This volume deals with first and second order complex equations of hyperbolic and mixed types. Various general boundary value problems for linear and quasilinear complex equations are investigated in detail. To obtain results for complex equations of mixed types, some discontinuous boundary value problems for elliptic complex equations are discusse
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.
Boundary Value Problems Integral Equations And Related Problems
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Author : Guo Chun Wen
language : en
Publisher: World Scientific
Release Date : 2011
Boundary Value Problems Integral Equations And Related 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 2011 with Mathematics categories.
In this volume, we report new results about various boundary value problems for partial differential equations and functional equations, theory and methods of integral equations and integral operators including singular integral equations, applications of boundary value problems and integral equations to mechanics and physics, numerical methods of integral equations and boundary value problems, theory and methods for inverse problems of mathematical physics, Clifford analysis and related problems. Contributors include: L Baratchart, B L Chen, D C Chen, S S Ding, K Q Lan, A Farajzadeh, M G Fei, T Kosztolowicz, A Makin, T Qian, J M Rassias, J Ryan, C-Q Ru, P Schiavone, P Wang, Q S Zhang, X Y Zhang, S Y Du, H Y Gao, X Li, Y Y Qiao, G C Wen, Z T Zhang, and others.
Nonlinear Partial Differential Equations And Hyperbolic Wave Phenomena
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Author : Norske videnskaps-akademi. Research Program on Nonlinear Partial Differential Equations
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-10-01
Nonlinear Partial Differential Equations And Hyperbolic Wave Phenomena written by Norske videnskaps-akademi. Research Program on Nonlinear Partial Differential Equations 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 2010-10-01 with Mathematics categories.
This volume presents the state of the art in several directions of research conducted by renowned mathematicians who participated in the research program on Nonlinear Partial Differential Equations at the Centre for Advanced Study at the Norwegian Academy of Science and Letters, Oslo, Norway, during the academic year 2008-09. The main theme of the volume is nonlinear partial differential equations that model a wide variety of wave phenomena. Topics discussed include systems of conservation laws, compressible Navier-Stokes equations, Navier-Stokes-Korteweg type systems in models for phase transitions, nonlinear evolution equations, degenerate/mixed type equations in fluid mechanics and differential geometry, nonlinear dispersive wave equations (Korteweg-de Vries, Camassa-Holm type, etc.), and Poisson interface problems and level set formulations.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2008
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Real And Complex Clifford Analysis
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Author : Sha Huang
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-16
Real And Complex Clifford Analysis written by Sha Huang 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 2006-03-16 with Mathematics categories.
Clifford analysis, a branch of mathematics that has been developed since about 1970, has important theoretical value and several applications. In this book, the authors introduce many properties of regular functions and generalized regular functions in real Clifford analysis, as well as harmonic functions in complex Clifford analysis. It covers important developments in handling the incommutativity of multiplication in Clifford algebra, the definitions and computations of high-order singular integrals, boundary value problems, and so on. In addition, the book considers harmonic analysis and boundary value problems in four kinds of characteristic fields proposed by Luogeng Hua for complex analysis of several variables. The great majority of the contents originate in the authors’ investigations, and this new monograph will be interesting for researchers studying the theory of functions.
International Journal Of Applied Mathematics Statistics
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Author :
language : en
Publisher:
Release Date : 2007
International Journal Of Applied Mathematics Statistics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Applied mathematics categories.
Lectures On Deformation Quantisation From Moyal Product To Kontsevich S Formality Theorem
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Author : Georgy Igorevich Sharygin
language : en
Publisher: World Scientific
Release Date : 2025-05-20
Lectures On Deformation Quantisation From Moyal Product To Kontsevich S Formality Theorem written by Georgy Igorevich Sharygin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-20 with Science categories.
Principles of classical Hamiltonian mechanics say that the evolution of a dynamical system is determined by the Poisson bracket of observable functions with the given Hamiltonian function of the system. In Quantum Mechanics, these principles are modified so that the algebra of observable functions should be replaced by a noncommutative algebra of operators and the Poisson bracket by their commutator so that the canonical commutation relations hold. Thus, working with quantum systems, we must determine the 'quantisation' of our observables, i.e. to choose a noncommutative algebra whose elements would play the role of the observables. With some modifications, this question is the main content of the Deformation Quantisation problem formulated in 1978 by Flato and others.This book is based on the course that the author taught in the Fall semester of 2019 at Peking University. The main purpose of that course and of this book is to acquaint the reader with the vast scope of ideas related to the Deformation Quantisation of Poisson manifolds. The book begins with Quantum Mechanics and Moyal product formula and covers the three main constructions that solve the Deformation Quantisation problem: Lecomte and de Wilde deformation of symplectic manifolds, Fedosov's Quantisation theory and Kontsevich's formality theorem. In the appendices, the Tamarkin's proof of formality theorem is outlined.The book is written in a reader-friendly manner and is as self-contained as possible. It includes several sets of problems and exercises that will help the reader to master the material.
Lecture Notes On Calculus Of Variations
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Author : Kung-ching Chang
language : en
Publisher: World Scientific
Release Date : 2016-09-16
Lecture Notes On Calculus Of Variations written by Kung-ching Chang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-16 with Mathematics categories.
This is based on the course 'Calculus of Variations' taught at Peking University from 2006 to 2010 for advanced undergraduate to graduate students majoring in mathematics. The book contains 20 lectures covering both the theoretical background material as well as an abundant collection of applications. Lectures 1-8 focus on the classical theory of calculus of variations. Lectures 9-14 introduce direct methods along with their theoretical foundations. Lectures 15-20 showcase a broad collection of applications. The book offers a panoramic view of the very important topic on calculus of variations. This is a valuable resource not only to mathematicians, but also to those students in engineering, economics, and management, etc.