On the Mixed Problem for a Hyperbolic Equation

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Publisher : American Mathematical Soc.
ISBN 13 : 0821818120
Total Pages : 122 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis On the Mixed Problem for a Hyperbolic Equation by : Tadeusz Bałaban

Download or read book On the Mixed Problem for a Hyperbolic Equation written by Tadeusz Bałaban and published by American Mathematical Soc.. This book was released on 1971 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.

Mixed Problems for Higher Order Hyperbolic Equations

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Publisher :
ISBN 13 :
Total Pages : 1 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis Mixed Problems for Higher Order Hyperbolic Equations by : Shmuel Agmon

Download or read book Mixed Problems for Higher Order Hyperbolic Equations written by Shmuel Agmon and published by . This book was released on 1962 with total page 1 pages. Available in PDF, EPUB and Kindle. Book excerpt: DESCRIPTORS: *Boundary layer, *Jets, Fluid flow, Reynolds number, Laminar boundary layer, Frequency, Flu ter, Excitation, Noz zles, Wave characteristics, Stability, Vis cosity, Vortices. An attempt is made to explain the development of vortices in a separated boundary layer by investigating the axisymmetrical jet downstream of a special nozzle. According to stability theory, a shear profile of finite thickness is unstable against wavy disturbances of certain frequencies and wavelengths. If such wavy disturbances are present in the shear layer, it rolls up into discrete vortices according to Rosenhead's analysis. It is found that viscosity, though responsible for the formation of a shear layer, plays no significant role in the process of rolling up at high Reynolds numbers. The frequency of the natural fluctuations and the relation between frequency and wavelength for artificial excita ion have been measured; the re ults are in good agreement with the theory. (Author).

Mixed Problems for Hyperbolic Equations

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Publisher :
ISBN 13 :
Total Pages : 212 pages
Book Rating : 4.:/5 (3 download)

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Book Synopsis Mixed Problems for Hyperbolic Equations by : Alberto Baider

Download or read book Mixed Problems for Hyperbolic Equations written by Alberto Baider and published by . This book was released on 1971 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Hyperbolic Boundary Value Problems

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Publisher : CUP Archive
ISBN 13 : 9780521235686
Total Pages : 232 pages
Book Rating : 4.2/5 (356 download)

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Book Synopsis Hyperbolic Boundary Value Problems by : Reiko Sakamoto

Download or read book Hyperbolic Boundary Value Problems written by Reiko Sakamoto and published by CUP Archive. This book was released on 1982-07-08 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Elliptic, Hyperbolic and Mixed Complex Equations with Parabolic Degeneracy

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Publisher : World Scientific
ISBN 13 : 9812779434
Total Pages : 453 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Elliptic, Hyperbolic and Mixed Complex Equations with Parabolic Degeneracy by : Guo Chun Wen

Download or read book Elliptic, Hyperbolic and Mixed Complex Equations with Parabolic Degeneracy written by Guo Chun Wen and published by World Scientific. This book was released on 2008 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Some Problems On Nonlinear Hyperbolic Equations And Applications

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Publisher : World Scientific
ISBN 13 : 981446404X
Total Pages : 464 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Some Problems On Nonlinear Hyperbolic Equations And Applications by : Tatsien Li

Download or read book Some Problems On Nonlinear Hyperbolic Equations And Applications written by Tatsien Li and published by World Scientific. This book was released on 2010-09-21 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is composed of two parts: Mathematical and Numerical Analysis for Strongly Nonlinear Plasma Models and Exact Controllability and Observability for Quasilinear Hyperbolic Systems and Applications. It presents recent progress and results obtained in the domains related to both subjects without attaching much importance to the details of proofs but rather to difficulties encountered, to open problems and possible ways to be exploited. It will be very useful for promoting further study on some important problems in the future.

The Dirichlet Problem for Elliptic-Hyperbolic Equations of Keldysh Type

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Publisher : Springer Science & Business Media
ISBN 13 : 3642244149
Total Pages : 219 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis The Dirichlet Problem for Elliptic-Hyperbolic Equations of Keldysh Type by : Thomas H. Otway

Download or read book The Dirichlet Problem for Elliptic-Hyperbolic Equations of Keldysh Type written by Thomas H. Otway and published by Springer Science & Business Media. This book was released on 2012-01-07 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Partial differential equations of mixed elliptic-hyperbolic type arise in diverse areas of physics and geometry, including fluid and plasma dynamics, optics, cosmology, traffic engineering, projective geometry, geometric variational theory, and the theory of isometric embeddings. And yet even the linear theory of these equations is at a very early stage. This text examines various Dirichlet problems which can be formulated for equations of Keldysh type, one of the two main classes of linear elliptic-hyperbolic equations. Open boundary conditions (in which data are prescribed on only part of the boundary) and closed boundary conditions (in which data are prescribed on the entire boundary) are both considered. Emphasis is on the formulation of boundary conditions for which solutions can be shown to exist in an appropriate function space. Specific applications to plasma physics, optics, and analysis on projective spaces are discussed. (From the preface)

Generalized Goursat Problem for a Hyperbolic System

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Publisher :
ISBN 13 :
Total Pages : 182 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Generalized Goursat Problem for a Hyperbolic System by : Robert P.. Holten

Download or read book Generalized Goursat Problem for a Hyperbolic System written by Robert P.. Holten and published by . This book was released on 1958 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Hyperbolic Equations and Waves

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Publisher : Springer Science & Business Media
ISBN 13 : 3642870252
Total Pages : 403 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Hyperbolic Equations and Waves by : Marcel Froissart

Download or read book Hyperbolic Equations and Waves written by Marcel Froissart and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: The success of the 1967 Battelle Rencontres was so much appre ciated by the participants and organizers of this experimental set-up that it was soon decided to go on with the experiment. Mathematicians and physicists had found a very suitable frame to overcome their natural shyness, to get occasionally interested into each others' work, to talk 1968 Rencontres have about it, and eventually to know each other. The been organized with the same idea in mind, and even somewhat enlarged in the following sense: the topic chosen - hyperbolic equations and waves - has proved a cornerstone of physics for more than a century and extends over most fields of contemporary physics. It follows immediately that the wide range of physicists concerned could not be represented by more than a couple of specialists in any single field. Thus, aside from bridging the gap between mathematicians and physicists, the 1968 Recontres provided a rather unique occasion to plug many intra disciplinary gaps among physicists. This made the Rencontres quite unpredictable as to how people would - and could - interact, and created a very stimulating environ ment for an unprecedented intellectual venture. From the outside, it may very well look like a hodge-podge of quite unrelated ideas. But it was much less so at the level of day-to-day discussions and informal gatherings where all slowly acquired a comprehensive synthetic view of the subject.

Singularities in Boundary Value Problems

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Publisher : Springer Science & Business Media
ISBN 13 : 9400984340
Total Pages : 390 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Singularities in Boundary Value Problems by : H.G. Garnir

Download or read book Singularities in Boundary Value Problems written by H.G. Garnir and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 1980 Maratea NATO Advanced Study Institute (= ASI) followed the lines of the 1976 Liege NATO ASI. Indeed, the interest of boundary problems for linear evolution partial differential equations and systems is more and more acute because of the outstanding position of those problems in the mathematical description of the physical world, namely through sciences such as fluid dynamics, elastodynamics, electro dynamics, electromagnetism, plasma physics and so on. In those problems the question of the propagation of singularities of the solution has boomed these last years. Placed in its definitive mathematical frame in 1970 by L. Hormander, this branch -of the theory recorded a tremendous impetus in the last decade and is now eagerly studied by the most prominent research workers in the field of partial differential equations. It describes the wave phenomena connected with the solution of boundary problems with very general boundaries, by replacing the (generailly impossible) computation of a precise solution by a convenient asymptotic approximation. For instance, it allows the description of progressive waves in a medium with obstacles of various shapes, meeting classical phenomena as reflexion, refraction, transmission, and even more complicated ones, called supersonic waves, head waves, creeping waves, •••••• The !'tudy of singularities uses involved new mathematical concepts (such as distributions, wave front sets, asymptotic developments, pseudo-differential operators, Fourier integral operators, microfunctions, ••• ) but emerges as the most sensible application to physical problems. A complete exposition of the present state of this theory seemed to be still lacking.

Multi-dimensional Hyperbolic Partial Differential Equations

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Publisher : Oxford University Press, USA
ISBN 13 : 019921123X
Total Pages : 535 pages
Book Rating : 4.1/5 (992 download)

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Book Synopsis Multi-dimensional Hyperbolic Partial Differential Equations by : Sylvie Benzoni-Gavage

Download or read book Multi-dimensional Hyperbolic Partial Differential Equations written by Sylvie Benzoni-Gavage and published by Oxford University Press, USA. This book was released on 2007 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Integral Geometry and Inverse Problems for Hyperbolic Equations

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Publisher : Springer Science & Business Media
ISBN 13 : 364280781X
Total Pages : 160 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Integral Geometry and Inverse Problems for Hyperbolic Equations by : V. G. Romanov

Download or read book Integral Geometry and Inverse Problems for Hyperbolic Equations written by V. G. Romanov and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are currently many practical situations in which one wishes to determine the coefficients in an ordinary or partial differential equation from known functionals of its solution. These are often called "inverse problems of mathematical physics" and may be contrasted with problems in which an equation is given and one looks for its solution under initial and boundary conditions. Although inverse problems are often ill-posed in the classical sense, their practical importance is such that they may be considered among the pressing problems of current mathematical re search. A. N. Tihonov showed [82], [83] that there is a broad class of inverse problems for which a particular non-classical definition of well-posed ness is appropriate. This new definition requires that a solution be unique in a class of solutions belonging to a given subset M of a function space. The existence of a solution in this set is assumed a priori for some set of data. The classical requirement of continuous dependence of the solution on the data is retained but it is interpreted differently. It is required that solutions depend continuously only on that data which does not take the solutions out of M.

Hyperbolic Equations and Related Topics

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Publisher : Academic Press
ISBN 13 : 1483269256
Total Pages : 458 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Hyperbolic Equations and Related Topics by : Sigeru Mizohata

Download or read book Hyperbolic Equations and Related Topics written by Sigeru Mizohata and published by Academic Press. This book was released on 2014-05-10 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Hyperbolic Problems: Theory, Numerics, Applications

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Publisher : Birkhäuser
ISBN 13 : 3034887248
Total Pages : 514 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Hyperbolic Problems: Theory, Numerics, Applications by : Michael Fey

Download or read book Hyperbolic Problems: Theory, Numerics, Applications written by Michael Fey and published by Birkhäuser. This book was released on 2012-12-06 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: [Infotext]((Kurztext))These are the proceedings of the 7th International Conference on Hyperbolic Problems, held in Zürich in February 1998. The speakers and contributors have been rigorously selected and present the state of the art in this field. The articles, both theoretical and numerical, encompass a wide range of applications, such as nonlinear waves in solids, various computational fluid dynamics from small-scale combustion to relativistic astrophysical problems, multiphase phenomena and geometrical optics. ((Volltext))These proceedings contain, in two volumes, approximately one hundred papers presented at the conference on hyperbolic problems, which has focused to a large extent on the laws of nonlinear hyperbolic conservation. Two-fifths of the papers are devoted to mathematical aspects such as global existence, uniqueness, asymptotic behavior such as large time stability, stability and instabilities of waves and structures, various limits of the solution, the Riemann problem and so on. Roughly the same number of articles are devoted to numerical analysis, for example stability and convergence of numerical schemes, as well as schemes with special desired properties such as shock capturing, interface fitting and high-order approximations to multidimensional systems. The results in these contributions, both theoretical and numerical, encompass a wide range of applications such as nonlinear waves in solids, various computational fluid dynamics from small-scale combustion to relativistic astrophysical problems, multiphase phenomena and geometrical optics.

Mixed Initial and Boundary Value Problem in Linear Hyperbolic Partial Differential Equations of Higher Order in Two Dimensions

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Publisher :
ISBN 13 :
Total Pages : 66 pages
Book Rating : 4.:/5 (551 download)

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Book Synopsis Mixed Initial and Boundary Value Problem in Linear Hyperbolic Partial Differential Equations of Higher Order in Two Dimensions by : Gideon Peyser

Download or read book Mixed Initial and Boundary Value Problem in Linear Hyperbolic Partial Differential Equations of Higher Order in Two Dimensions written by Gideon Peyser and published by . This book was released on 1957 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Boundary Value Problems for Linear Evolution Partial Differential Equations

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Publisher : Springer Science & Business Media
ISBN 13 : 9401012059
Total Pages : 484 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis Boundary Value Problems for Linear Evolution Partial Differential Equations by : H.G. Garnir

Download or read book Boundary Value Problems for Linear Evolution Partial Differential Equations written by H.G. Garnir and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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,,

Transmutation, Scattering Theory and Special Functions

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Publisher : Elsevier
ISBN 13 : 0080871801
Total Pages : 469 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Transmutation, Scattering Theory and Special Functions by : R. Carroll

Download or read book Transmutation, Scattering Theory and Special Functions written by R. Carroll and published by Elsevier. This book was released on 2011-08-18 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transmutation, Scattering Theory and Special Functions