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: 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: Tosio Katō
Publisher:
ISBN:
Category : Differential equations, Elliptic
Languages : en
Pages : 87
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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.
Author: Aleksandr Mikhaĭlovich Blokhin
Publisher: Nova Publishers
ISBN: 9781560725923
Category : Mathematics
Languages : en
Pages : 140
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Book Description
Contents: Mixed problems for the wave equation in co-ordinate corner with additional condition on edge; Well-posedness of mixed problems for wave equation and general hyperbolic equation of second order in co-ordinate corner; Ill-posedness examples in mixed problem; Mixed problem for wave equation in co-ordinate corner -- problem (B0). Solvability condition. Exact solution. A priori estimate in W1/2 (R ); Obtaining of a priori estimate in mixed problems for the multidimensional wave equation.
Author: H.G. Garnir
Publisher: Springer Science & Business Media
ISBN: 9401012059
Category : Mathematics
Languages : en
Pages : 484
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Book Description
Most of the problems posed by Physics to Mathematical Analysis are boundary value problems for partial differential equations and systems. Among them, the problems concerning linear evolution equations have an outstanding position in the study of the physical world, namely in fluid dynamics, elastodynamics, electromagnetism, plasma physics and so on. This Institute was devoted to these problems. It developed essentially the new methods inspired by Functional Analysis and specially by the theories of Hilbert spaces, distributions and ultradistributions. The lectures brought a detailed exposition of the novelties in this field by world known specialists. We held the Institute at the Sart Tilman Campus of the University of Liege from September 6 to 17, 1976. It was attended by 99 participants, 79 from NATO Countries [Belgium (30), Canada (2), Denmark (I), France (15), West Germany (9), Italy (5), Turkey (3), USA (14)] and 20 from non NATO Countries [Algeria (2), Australia (3), Austria (I), Finland (1), Iran (3), Ireland (I), Japan (6), Poland (1), Sweden (I), Zair (1)]. There were 5 courses of_ 6_ h. ollI'. s~. 1. nL lJ. , h. t;l. l. I. rl"~, 1. n,L ,_ h. t;l. l. I. r. !'~ , ?_ n. f~ ?_ h,,
Author: Sigeru Mizohata
Publisher: Academic Press
ISBN: 1483269256
Category : Mathematics
Languages : en
Pages : 458
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Book Description
Hyperbolic Equations and Related Topics covers the proceedings of the Taniguchi International Symposium, held in Katata, Japan on August 27-31, 1984 and in Kyoto, Japan on September 3-5, 1984. The book focuses on the mathematical analyses involved in hyperbolic equations. The selection first elaborates on complex vector fields; holomorphic extension of CR functions and related problems; second microlocalization and propagation of singularities for semi-linear hyperbolic equations; and scattering matrix for two convex obstacles. Discussions focus on the construction of asymptotic solutions, singular vector fields and Leibniz formula, second microlocalization along a Lagrangean submanifold, and hypo-analytic structures. The text then ponders on the Cauchy problem for effectively hyperbolic equations and for uniformly diagonalizable hyperbolic systems in Gevrey classes. The book takes a look at generalized Hamilton flows and singularities of solutions of the hyperbolic Cauchy problem and analytic and Gevrey well-posedness of the Cauchy problem for second order weakly hyperbolic equations with coefficients irregular in time. The selection is a dependable reference for researchers interested in hyperbolic equations.
Author: Nikolaĭ Nikolaevich Bogoli︠u︡bov
Publisher: Benjamin-Cummings Publishing Company
ISBN:
Category : Science
Languages : en
Pages : 424
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Book Description
Author: C.M. Dafermos
Publisher: Elsevier
ISBN: 0080461387
Category : Mathematics
Languages : en
Pages : 677
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Book Description
The aim of this Handbook is to acquaint the reader with the current status of the theory of evolutionary partial differential equations, and with some of its applications. Evolutionary partial differential equations made their first appearance in the 18th century, in the endeavor to understand the motion of fluids and other continuous media. The active research effort over the span of two centuries, combined with the wide variety of physical phenomena that had to be explained, has resulted in an enormous body of literature. Any attempt to produce a comprehensive survey would be futile. The aim here is to collect review articles, written by leading experts, which will highlight the present and expected future directions of development of the field. The emphasis will be on nonlinear equations, which pose the most challenging problems today.. Volume I of this Handbook does focus on the abstract theory of evolutionary equations. . Volume 2 considers more concrete problems relating to specific applications. . Together they provide a panorama of this amazingly complex and rapidly developing branch of mathematics.
Author: Feliz Manuel Minhós
Publisher: MDPI
ISBN: 3036507108
Category : Mathematics
Languages : en
Pages : 158
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Book Description
This Special Edition contains new results on Differential and Integral Equations and Systems, covering higher-order Initial and Boundary Value Problems, fractional differential and integral equations and applications, non-local optimal control, inverse, and higher-order nonlinear boundary value problems, distributional solutions in the form of a finite series of the Dirac delta function and its derivatives, asymptotic properties’ oscillatory theory for neutral nonlinear differential equations, the existence of extremal solutions via monotone iterative techniques, predator–prey interaction via fractional-order models, among others. Our main goal is not only to show new trends in this field but also to showcase and provide new methods and techniques that can lead to future research.
