A Uniqueness Theorem For Second Order Hyperbolic Differential Equations
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A Uniqueness Theorem For Second Order Hyperbolic Differential Equations
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Author : Lars Hörmander
language : en
Publisher:
Release Date : 1991
A Uniqueness Theorem For Second Order Hyperbolic Differential Equations written by Lars Hörmander and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with categories.
Uniqueness Theory For Linear Hyperbolic Partial Differential Equations
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Author : Charles Raymond De Prima
language : en
Publisher:
Release Date : 1948
Uniqueness Theory For Linear Hyperbolic Partial Differential Equations written by Charles Raymond De Prima and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1948 with Differential equations, Linear categories.
Proof Of An Existence And Uniqueness Theorem Of Picard For A Non Linear Hyperbolic Partial Differential Equation By Means Of An Analogue Of Cauchy S Polygon Method
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Author : Robert H. Moore
language : en
Publisher:
Release Date : 1956
Proof Of An Existence And Uniqueness Theorem Of Picard For A Non Linear Hyperbolic Partial Differential Equation By Means Of An Analogue Of Cauchy S Polygon Method written by Robert H. Moore and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1956 with Cauchy problem categories.
Following the general method used in proving the existence and uniqueness of the solution of the Cauchy problem for the first order ordinary differential equation by means of Cauchy polygons of approximation, the present paper proves the existence and uniqueness of the solution of an analogous boundary value problem for a second order hyperbolic partial differential equation by means of approximate solutions which are essentially surfaces of approximation. As in the method for the ordinary equation, a set of convergence inequalities is first obtained, and then it is shown, by means of these inequalities, that the sequence of approximate solutions defined converges uniformly to a unique solution of the hyperbolic equation.
Lectures On Nonlinear Hyperbolic Differential Equations
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Author : Lars Hörmander
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-07-17
Lectures On Nonlinear Hyperbolic Differential Equations written by Lars Hörmander 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 1997-07-17 with Mathematics categories.
In this introductory textbook, a revised and extended version of well-known lectures by L. Hörmander from 1986, four chapters are devoted to weak solutions of systems of conservation laws. Apart from that the book only studies classical solutions. Two chapters concern the existence of global solutions or estimates of the lifespan for solutions of nonlinear perturbations of the wave or Klein-Gordon equation with small initial data. Four chapters are devoted to microanalysis of the singularities of the solutions. This part assumes some familiarity with pseudodifferential operators which are standard in the theory of linear differential operators, but the extension to the more exotic classes of opertors needed in the nonlinear theory is presented in complete detail.
Uniqueness And Existence Theorems For Linear Symmetric Hyperbolic Systems Of First Order Partial Differential Equations By The Method Of Energy Integrals
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Author : Ronald E. Dean
language : en
Publisher:
Release Date : 1967
Uniqueness And Existence Theorems For Linear Symmetric Hyperbolic Systems Of First Order Partial Differential Equations By The Method Of Energy Integrals written by Ronald E. Dean and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with categories.
Carleman Estimates For Second Order Partial Differential Operators And Applications
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Author : Xiaoyu Fu
language : en
Publisher: Springer Nature
Release Date : 2019-10-31
Carleman Estimates For Second Order Partial Differential Operators And Applications written by Xiaoyu Fu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-31 with Mathematics categories.
This book provides a brief, self-contained introduction to Carleman estimates for three typical second order partial differential equations, namely elliptic, parabolic, and hyperbolic equations, and their typical applications in control, unique continuation, and inverse problems. There are three particularly important and novel features of the book. First, only some basic calculus is needed in order to obtain the main results presented, though some elementary knowledge of functional analysis and partial differential equations will be helpful in understanding them. Second, all Carleman estimates in the book are derived from a fundamental identity for a second order partial differential operator; the only difference is the choice of weight functions. Third, only rather weak smoothness and/or integrability conditions are needed for the coefficients appearing in the equations. Carleman Estimates for Second Order Partial Differential Operators and Applications will be of interest to all researchers in the field.
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.
Multi Dimensional Hyperbolic Partial Differential Equations
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Author : Sylvie Benzoni-Gavage
language : en
Publisher: Oxford University Press, USA
Release Date : 2007
Multi Dimensional Hyperbolic Partial Differential Equations written by Sylvie Benzoni-Gavage and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Authored by leading scholars, this comprehensive text presents a view of the multi-dimensional hyperbolic partial differential equations, with a particular emphasis on problems in which modern tools of analysis have proved useful. It is useful to graduates and researchers in both hyperbolic PDEs and compressible fluid dynamics.
Existence Theorems In Partial Differential Equations
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Author : Dorothy L. Bernstein
language : en
Publisher: Princeton University Press
Release Date : 1951-01-20
Existence Theorems In Partial Differential Equations written by Dorothy L. Bernstein and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1951-01-20 with Mathematics categories.
The description for this book, Existence Theorems in Partial Differential Equations. (AM-23), Volume 23, will be forthcoming.
Hyperbolic Differential Operators And Related Problems
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Author : Vincenzo Ancona
language : en
Publisher: CRC Press
Release Date : 2003-03-06
Hyperbolic Differential Operators And Related Problems written by Vincenzo Ancona and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-06 with Mathematics categories.
Presenting research from more than 30 international authorities, this reference provides a complete arsenal of tools and theorems to analyze systems of hyperbolic partial differential equations. The authors investigate a wide variety of problems in areas such as thermodynamics, electromagnetics, fluid dynamics, differential geometry, and topology. Renewing thought in the field of mathematical physics, Hyperbolic Differential Operators defines the notion of pseudosymmetry for matrix symbols of order zero as well as the notion of time function. Surpassing previously published material on the topic, this text is key for researchers and mathematicians specializing in hyperbolic, Schrödinger, Einstein, and partial differential equations; complex analysis; and mathematical physics.