Download or read book Asymptotic Methods for the Solution of Dispersive Hyperbolic Equations written by Robert Mervin Lewis and published by . This book was released on 1964 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general method is presented for finding asymptotic solutions of initial-boundary value problems for linear hyperbolic partial differential equations. A large parameter lambda appears in the equation, multiplying a lower order (dispersive) term. It also may appear in the initial data and the inhomogeneous (source) term, in a variety of ways. This gives rise to a variety of different types of asymptotic solutions. The expansion procedure is a ray method, i.e., all of the functions that appear in the expansion satisfy ordinary differential equations along certain space-time curves called rays. These rays do not lie on characteristic hypersurfaces, but instead fill out the interior of the characteristic hypercone. They are associated with an appropriately defined group velocity. The details of the expansion are presented for a simple second order hyperbolic equation. The applicability of the method to symmetric hyperbolic systems and to the integro-differential equations for dispersive dielectrics is discussed. (Author).

Download or read book Asymptotic Methods for the Solution of Initial boundary Value Problems for Dispersive Hyperbolic Equations written by Norman Bleistein and published by . This book was released on 1965 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Asymptotic Solution of a Dispersive Hyperbolic Equation With Variable Coefficients Classic Reprint written by Norman Bleistein and published by Forgotten Books. This book was released on 2018-02-07 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Asymptotic Solution of a Dispersive Hyperbolic Equation With Variable Coefficients In the past few years there has been a great deal of interest in the asymptotic expansion of solutions of boundary value problems and initial boundary value problems for partial differential equations. These expansions are obtained for large distance and/or time or for large values of a parameter which may appear naturally in the equation and/or initial conditions, boundary conditions, etc. Many of these problems can be treated by a method in which special curves, called rays, in space or space-time plan an essential role. The asymptotic solution is determined in terms of amplitude and phase functions which satis fy ordinary differential equations on these rays. These equations can often be solved explicitly, so that the solution to the original problem is known if the initial values on the rays of the amplitude and phase functions are known. In some cases these initial values can be determined directly from the data initial conditions, boundary conditions, etc.) of the given problem, while in other situations an indirect method is necessary. This method involves the exact solution of a canonical problem i.a., a problem simpler than that given originally but having the same local features as the given problem. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Download or read book Asymptotic Methods for the Solution of Dispersive Hyberbolic Equations Classic Reprint written by Robert M. Lewis and published by Forgotten Books. This book was released on 2018-01-30 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Asymptotic Methods for the Solution of Dispersive Hyberbolic Equations An important class of asymptotic methods is characterized by the fact that certain curves, often called rays, play a central role in the theory. The rays are of fundamental importance because all of the functions which make up the various terms of the expansion can be shown to satisfy ordinary differential equations along these curves. Thus, in a sense, the method is one which reduces partial differential equations to ordinary differential equations. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Download or read book Asymptotic Methods for the Solu of Dispersive Hyperbolic Equations written by Robert M. Lewis and published by . This book was released on 1964 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Asymptotic Expansions of Solutions of Initial Boundary Value Problems for a Dispersive Hyperbolic Equation Classic Reprint written by Norman Bleistein and published by Forgotten Books. This book was released on 2018-10-10 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Asymptotic Expansions of Solutions of Initial-Boundary Value Problems for a Dispersive Hyperbolic Equation Recently, the ray method has been applied to time dependent problems and in particular, dispersive hyperbolic equations A particular equation of this type, the klein-gordon equation, may be used to describe the propagation of electromagnetic waves in certain plasmas Initial-boundary value problems for this equation are presently being studied, since it is the simplest example of a large class of dispersive hyperbolic equations. As of now, there is no general proof that the ray method actually yields the asymptotic expansion of the exact solution. The purpose of the research in this paper is to compare the leading term of the asymptotic expansion of the exact solution and the ray solution for particular problems. The results are shown to agree and thereby add to the overwhelming evidence that the ray method is valid. We consider initial - boundary value problems in two space dimensions for the klein-gordon equation. The boundary is a parabola and.we require that the solution satisfy a homogeneous condition. The total solution is assumed to consist of a sum of a primary field and a reflected field. The associated rays are called primary and reflected rays and are straight lines in space time. The primary field must satisfy the equation and the initial conditions. The reflected field is taken to be zero initially and is determined at the boundary in such a way that the total solution satisfies the given boundary condition. The primary rays are emitted from the plane t O in space-time. For each primary ray incident on the boundary, a reflected ray is produced. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Download or read book Asymptotic Analysis for Nonlinear Dispersive and Wave Equations written by Keiichi Kato and published by Advanced Studies in Pure Mathe. This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is edited as the proceedings of the international conference 'Asymptotic Analysis for Nonlinear Dispersive and Wave Equations' held in September, 2014 at Department of Mathematics, Osaka University, Osaka, Japan. The conference was devoted to the honor of Professor Nakao Hayashi (Osaka University) on the occasion of his 60th birth year, and includes the newest results up to 2017 related to the fields of nonlinear partial differential equations of hyperbolic and dispersive type. In particular, the asymptotic expansion of solutions for those equations has been the main contribution of Professor Hayashi and his collaborators. The contents is 18 papers related to the asymptotic analysis and qualitative research paper concerning the problems of nonlinear wave equations and nonlinear dispersive equations such as nonlinear Schrödinger equations, the Hartree equation, the Camassa-Holm equation, the Ginzburg-Landau equations. Among others, the outstanding method developed by Professor Hayashi and his collaborators is introduced by one of his main collaborator, Professor P I Naumkin.This volume is suitable for any students and young researchers who are starting the research on the asymptotic analysis of nonlinear wave and dispersive equations for knowing the out-lined theory of these fields.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America

Download or read book Asymptotic Solution of a Dispersive Hyperbolic Equation with Variable Coefficients written by Norman Bleistein and published by . This book was released on 1965 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: Initial-boundary value problems are considered for an energy conserving dispersive hyperbolic equation, the Klein-Gordon equation. This equation contains the main feature of dispersion: The speed of propagation depends on the frequency. The asymptotic expansion of solutions obtained by a technique which we call the ray method is compared with the asymptotic expansion of the exact solution. In every case considered, the solutions agree. Solutions are obtained for a series of initial-boundary value problems in one space dimension with variable coefficients. A new feature which is called space-time diffraction is found. This phenomenon has the following physical interpretation: A portion of the energy of a wave reaches a boundary surface and then gradually leaks off, leaving a diminishing residue on the boundary for all time. (Author).

Download or read book Asymptotic Expansions of Solutions of Initial boundary Value Problems for a Dispersive Hyperbolic Equation written by Norman Bleistein and published by . This book was released on 1965 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: Initial-boundary value problems for an energy conserving dispersive hyperbolic equation, the Klein-Gordon equation, are considered. This equation exhibits the main feature of dispersion: The speed of propagation depends on frequency. Problems in two space dimensions with a parabolic boundary are discussed. The primary purpose of this paper is to compare the asymptotic expansion of solutions obtained by a technique we call the ray method with the asymptotic expansion of the exact solution. In the cases considered, the solutions agree. In addition a numerical comparison is made of the exact and asymptotic solutions for a specified region of space time. (Author).

Download or read book Asymptotic Analysis and Singularities Hyperbolic and dispersive PDEs and fluid mechanics written by Hideo Kozono and published by . This book was released on 2007 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the proceedings of the 14th MSJ International Research Institute "Asymptotic Analysis and Singularity", which was held at Sendai, Japan in July 2005. The proceedings contain survey papers and original research papers on nonlinear partial differential equations, dynamical systems, calculus of variations and mathematical physics.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America

Download or read book Asymptotic Methods for Investigating Quasiwave Equations of Hyperbolic Type written by Yuri A. Mitropolsky and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of partial differential equations is a wide and rapidly developing branch of contemporary mathematics. Problems related to partial differential equations of order higher than one are so diverse that a general theory can hardly be built up. There are several essentially different kinds of differential equations called elliptic, hyperbolic, and parabolic. Regarding the construction of solutions of Cauchy, mixed and boundary value problems, each kind of equation exhibits entirely different properties. Cauchy problems for hyperbolic equations and systems with variable coefficients have been studied in classical works of Petrovskii, Leret, Courant, Gording. Mixed problems for hyperbolic equations were considered by Vishik, Ladyzhenskaya, and that for general two dimensional equations were investigated by Bitsadze, Vishik, Gol'dberg, Ladyzhenskaya, Myshkis, and others. In last decade the theory of solvability on the whole of boundary value problems for nonlinear differential equations has received intensive development. Significant results for nonlinear elliptic and parabolic equations of second order were obtained in works of Gvazava, Ladyzhenskaya, Nakhushev, Oleinik, Skripnik, and others. Concerning the solvability in general of nonlinear hyperbolic equations, which are connected to the theory of local and nonlocal boundary value problems for hyperbolic equations, there are only partial results obtained by Bronshtein, Pokhozhev, Nakhushev.

Download or read book Uniform Asymptotic Solutions of Discontinuous Initial Value Problems for Dispersive Hyperbolic Equations written by J. Boersma and published by . This book was released on 1967 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters written by H.G. Kaper and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the NATO Advanced Research Workshop on "Asymptotic-induced Numerical Methods for Partial Differ ential Equations, Critical Parameters, and Domain Decomposition," held at Beaune (France), May 25-28, 1992. The purpose of the workshop was to stimulate the integration of asymp totic analysis, domain decomposition methods, and symbolic manipulation tools for the numerical solution of partial differential equations (PDEs) with critical parameters. A workshop on the same topic was held at Argonne Na tional Laboratory in February 1990. (The proceedings were published under the title Asymptotic Analysis and the Numerical Solu.tion of Partial Differ ential Equations, Hans G. Kaper and Marc Garbey, eds., Lecture Notes in Pure and Applied Mathematics. Vol. 130, ·Marcel Dekker, Inc., New York, 1991.) In a sense, the present proceedings represent a progress report on the topic area. Comparing the two sets of proceedings, we see an increase in the quantity as well as the quality of the contributions. 110re research is being done in the topic area, and the interest covers serious, nontrivial problems. We are pleased with this outcome and expect to see even more advances in the next few years as the field progresses.

Download or read book Asymptotic Expansions of Solutions of Initial Boundary Value Problems for a Dispersive Hyperbolic Equation Primary Source Edition written by Norman Bleistein and published by Nabu Press. This book was released on 2013-12 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book.

Download or read book Asymptotic Analysis and the Numerical Solution of Partial Differential Equations written by Hans G. Kaper and published by CRC Press. This book was released on 1991-02-25 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integrates two fields generally held to be incompatible, if not downright antithetical, in 16 lectures from a February 1990 workshop at the Argonne National Laboratory, Illinois. The topics, of interest to industrial and applied mathematicians, analysts, and computer scientists, include singular per

Download or read book Asymptotic Methods in Equations of Mathematical Physics written by B Vainberg and published by CRC Press. This book was released on 1989-02-25 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: Typed English translation of a monograph first published (in Russian) in 1982. Provides graduate students and researchers with usefully detailed discussion of most of the asymptotic methods standard these days to the work of mathematical physicists. The author prefers not to dwell in the heights of abstraction; he has written a broadly intelligble book, which is informed at every point by his secure command of major physical applications. An expensive but valuable contribution to the literature of an important but too-little-written- about field. Twelve chapters, references. (NW) Annotation copyrighted by Book News, Inc., Portland, OR

Download or read book U S Government Research Reports written by and published by . This book was released on 1964 with total page 1310 pages. Available in PDF, EPUB and Kindle. Book excerpt: