3 edition of Hyperbolic equations found in the catalog.
Conference on Hyperbolic Equations and Related Topics (1985 University of Padova)
|Statement||F. Colombini & M.K.V. Murthy, editors.|
|Series||Pitman research notes in mathematics series,, 158|
|Contributions||Colombini, F., Murthy, M. K. V.|
|LC Classifications||QA377 .C7625 1985|
|The Physical Object|
|Pagination||286 p. ;|
|Number of Pages||286|
|ISBN 10||0582988918, 0470208694|
|LC Control Number||87002965|
In mathematics, a hyperbolic partial differential equation of order is a partial differential equation (PDE) that, roughly speaking, has a well-posed initial value problem for the first − derivatives. More precisely, the Cauchy problem can be locally solved for arbitrary initial data along any non-characteristic of the equations of mechanics are hyperbolic, and so the study. Most of the present books on pde analysis deal with the elliptic partial differential equations. Is there some book related to rigorous analysis with hyperbolic pdes, and especially hyperbolic syst.
Hyperbolic Partial Differential Equations and Geometric Optics Jeffrey Rauch This book introduces graduate students and researchers in mathematics and the sciences to the multifaceted subject of the equations of hyperbolic type, which are used, in particular, to describe propagation of . This book introduces graduate students and researchers in mathematics and the sciences to the multifaceted subject of the equations of hyperbolic type, which are used, in particular, to describe propagation of waves at finite speed. Among the topics carefully presented in the book are nonlinear geometric optics, the asymptotic analysis of short wavelength solutions, and nonlinear .
Introduction to Hyperbolic Functions This video provides a basic overview of hyperbolic function. The lesson defines the hyperbolic functions, shows the graphs of the hyperbolic functions, and gives the properties of hyperbolic functions. Hyperbolic functions are exponential functions that share similar properties to trigonometric functions. The book can be divided into two parts. In the first part, the results on decay of solutions to nonlinear parabolic equations and hyperbolic parabolic coupled systems are obtained, and a chapter is devoted to the global existence of small smooth solutions to fully nonlinear parabolic equations and quasilinear hyperbolic parabolic coupled systems.
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The theory of hyperbolic equations is a large subject, and Hyperbolic equations book 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 Author: Pavel B.
Bochev, Max D. Gunzburger. Other hyperbolic equations, both linear and nonlinear, exhibit many wave-like phenomena. The primary theme of this book is the mathematical investigation of such wave phenomena. The exposition begins with derivations of some wave equations, including waves in an elastic body, such as those observed in connection with by: The content of this book corresponds to a one-semester course taught at the University of Paris-Sud (Orsay) in the spring It is accessible to students or researchers with a basic elementary knowledge of Partial Dif ferential Equations, especially of hyperbolic PDE (Cauchy problem, wave operator, energy inequality, finite speed of propagation, symmetric systems, etc.).Cited by: Book Description.
Numerical Methods for Hyperbolic Equations is a collection of 49 articles presented at the International Conference on Numerical Methods for Hyperbolic Equations: Theory and Applications (Santiago de Compostela, Spain, July ).
The conference was organized to honour Professor Eleuterio Toro in the month of his 65th birthday. “This is an excellent book that can be used to introduce the reader to the theory of hyperbolic equations and to the mathematical theory of gravitational waves and Einstein equations.
Several basic concepts such as wavelike propagation, fundamental solution, Riemann kernel and its existence, world function and its role in the fundamental. Partly because it addresses nonlinear hyperbolic operators, and that is unusual. Almost any book in this subject would stay with the linear setting, and the hyperbolic non-linear notion is very tied to the field equations of Quantum Field Theory(QFT), which are usually hyperbolic and by: The solutions to hyperbolic equations tend to be more complex and interesting than those to parabolic and elliptic equations.
The interesting characteristics of the solutions to hyperbolic equations follows from the fact that the phenomena modeled by hyperbolic equations are. This volume contains the lecture notes of the Short Course on Numerical Methods for Hyperbolic Equations (Faculty of Mathematics, University of Santiago de Compostela, Spain, July ).
The course was organized in recognition of Prof. Eleuterio Toro’s contribution to education and training on numerical methods for partial differential equations and was organized prior to the.
hyperbolic system () reduces to a set of independent scalar hyperbolic equations. If B is not zero, then in general the resulting system of equations is coupled together, but only in the undifferentiated terms. The effect of the lower order term, Bu,is to cause.
In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions defined for the hyperbola rather than on the circle: just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the equilateral hyperbola.
Hyperbolic functions occur in the calculations of angles and distances in hyperbolic geometry. As was the case with the Laplace equation, mean value constructions are important for the wave equation, and they permit us to reduce the wave equation for d > 1 to the Darboux equation for the mean values, which is hyperbolic as well but involves only one spatial coordinate.
Purchase Hyperbolic Partial Differential Equations - 1st Edition. Print Book & E-Book. ISBNBook Edition: 1. Numerical Solution of Hyperbolic Partial Differential Equations is a new type of graduate textbook, comprising print, and interactive electronic components (on CD).
It is a comprehensive presentation of the modern theory and numerics with a range of applications broad enough to engage most engineering disciplines and many areas of applied Cited by: A distinctive aspect of numerical methods for hyperbolic equations is that they introduce errors which distort the physical nature of the phenomena under study.
Describing those errors by invoking concepts which originated in mathematical physics, such as energy propagation, dispersion and diffusion thus proves to be a most enlightening approach. Numerical Methods for Hyperbolic Equations is a collection of 49 articles presented at the International Conference on Numerical Methods for Hyperbolic Equations: Theory and Applications (Santiago de Compostela, Spain, July ).
The conference was organized to honour Professor Eleuterio Toro in the month of his 65th birthday. The topics coverCited by: 8. book we mainly follow the line of descriptions by K.
Chueh, C. Conley and J. Smoller with some modiﬁcations of proof. Applications to not only nonlinear parabolic equations but also some nonlinear hyperbolic equations are shown in this chapter.
During the s, a. About this book Introduction It is aimed at providing a comprehensive and up-to-date presentation of numerical methods which are nowadays used to solve nonlinear partial differential equations of hyperbolic type, developing shock discontinuities.
Book Description. Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrödinger Equations shows how four types of higher-order nonlinear evolution partial differential equations (PDEs) have many commonalities through their special quasilinear degenerate representations.
The authors present a unified approach to deal with these quasilinear PDEs. Hyperbolic nonconservative partial differential equations, such as the Von Foerster system, in which boundary conditions may depend upon the dependent variable (integral boundary conditions, for example) are solved by an approximation method based on similar work of the author for (nonlinear stochastic) ordinary differential equations.
The book represent a ﬁrst step aimed at a large and rich subject and I hope that readers are suﬃciently attracted to probe further.
§P A bird’s eye view of hyperbolic equations The central theme of this book is hyperbolic partial diﬀerential equations. These equations are.
HDG methods for time-harmonic hyperbolic equations are also strongly related to the HDG methods for steady-state diffusion problems.
The first HDG method for the Helmholtz equation was introduced by Griesmaier and Monk (). The same optimal convergence and superconvergence properties of the associated steady-state diffusion were proven.In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean parallel postulate of Euclidean geometry is replaced with.
For any given line R and point P not on R, in the plane containing both line R and point P there are at least two distinct lines through P that do not intersect R.Hyperbolic function are analogs of trigonometric function and they occur in the solution of many differential or cubic equations.
In contrast to trigonometric functions who form a circle, hyperbolic functions relate to a hyperbola. To demonstrate geometric representation of hyperbolic functions we’ll draw a hyperbola in Cartesian coordinate system.