On the Mixed Problem for a Hyperbolic Equation PDF Download
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Author: Tadeusz Bałaban
Publisher: American Mathematical Soc.
ISBN: 0821818120
Category : Boundary value problems
Languages : en
Pages : 122
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Book Description
"The aim of this paper is to present existence theorems for the mixed problem for a certain class of hyperbolic operators with boundary conditions. The subject was stimulated by S. Agmon's results (Les équations aux dérivées partielles (Paris, 1962)). He considered operators with constant coefficients in the principal part, and in domains bounded by suitable hyperplanes. We generalize his results to operators with variable coefficients, and to domains bounded by hypersurfaces."--from the author's introduction.
Author: Tadeusz Bałaban
Publisher: American Mathematical Soc.
ISBN: 0821818120
Category : Boundary value problems
Languages : en
Pages : 122
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Book Description
"The aim of this paper is to present existence theorems for the mixed problem for a certain class of hyperbolic operators with boundary conditions. The subject was stimulated by S. Agmon's results (Les équations aux dérivées partielles (Paris, 1962)). He considered operators with constant coefficients in the principal part, and in domains bounded by suitable hyperplanes. We generalize his results to operators with variable coefficients, and to domains bounded by hypersurfaces."--from the author's introduction.
Author:
Publisher:
ISBN: 9780821818121
Category :
Languages : en
Pages : 117
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Book Description
Author: Peter D. Lax
Publisher: American Mathematical Soc.
ISBN: 0821835769
Category : Mathematics
Languages : en
Pages : 234
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Book Description
The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theory and is an ideal text for a second-year graduate course on the subject. The first part deals with the basic theory: the relation of hyperbolicity to the finite propagation of signals, the concept and role of characteristic surfaces and rays, energy, and energy inequalities. The structure of solutions of equations with constant coefficients is explored with the help of the Fourier and Radon transforms. The existence of solutions of equations with variable coefficients with prescribed initial values is proved using energy inequalities. The propagation of singularities is studied with the help of progressing waves. The second part describes finite difference approximations of hyperbolic equations, presents a streamlined version of the Lax-Phillips scattering theory, and covers basic concepts and results for hyperbolic systems of conservation laws, an active research area today. Four brief appendices sketch topics that are important or amusing, such as Huygens' principle and a theory of mixed initial and boundary value problems. A fifth appendix by Cathleen Morawetz describes a nonstandard energy identity and its uses. -- Back cover.
Author: Tadeusz Balaban
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Semen Grigorʹevich Gindikin
Publisher: American Mathematical Soc.
ISBN: 9780821846179
Category : Mathematics
Languages : en
Pages : 233
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Book Description
This book offers the first systematic presentation of the theory of the mixed problem for hyperbolic differential equations with variable coefficients. This class includes hyperbolic and parabolic equations as well as nonclassic type of operator - the $q$-hyperbolic equation - which was introduced by the authors. As part of the exposition, the authors consider the Cauchy problem for this class of equations. This book would be suitable as a graduate textbook for courses in partial differential equations.
Author: A. V. Bitsadze
Publisher: Elsevier
ISBN: 1483164861
Category : Mathematics
Languages : en
Pages : 177
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Book Description
Equations of the Mixed Type compiles a series of lectures on certain fundamental questions in the theory of equations of mixed type. This book investigates the series of problems concerning linear partial differential equations of the second order in two variables, and possessing the property that the type of the equation changes either on the boundary of or inside the considered domain. Topics covered include general remarks on linear partial differential equations of mixed type; study of the solutions of second order hyperbolic equations with initial conditions given along the lines of parabolicity; and study of the solutions of second order elliptic equations for a domain, the boundary of which includes a segment of the curve of parabolic degeneracy. The problem of Tricomi and other mixed problems are also deliberated in this text. This publication is a good reference for students and researchers conducting work on the theory of equations of mixed type.
Author: Guo Chun Wen
Publisher: World Scientific
ISBN: 9812779434
Category : Mathematics
Languages : en
Pages : 453
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Book Description
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.
Author: Guo Chun Wen
Publisher: CRC Press
ISBN: 0203166582
Category : Mathematics
Languages : en
Pages : 272
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Book Description
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
Author: Alberto Baider
Publisher:
ISBN:
Category :
Languages : en
Pages : 212
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Book Description
Author: Reiko Sakamoto
Publisher: CUP Archive
ISBN: 9780521235686
Category : Mathematics
Languages : en
Pages : 232
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Book Description
Boundary value problems are of central importance and interest not only to mathematicians but also to physicists and engineers who need to solve differential equations which govern the behaviour of physical systems. In this book, Professor Sakamoto introduces the general theory of the existence and uniqueness of solutions to the wave equation. The reader is assumed to have some familiarity with Lebesgue integration and complex function theory but other than that the book is essentially self-contained. It is therefore suited to senior undergraduates and graduates in mathematics and the mathematical sciences but can be read with profit by professionals in those subjects.
