Download or read book The Cauchy Problem for the Linearised Einstein Equation and the Goursat Problem for Wave Equations written by Oliver Lindblad Petersen and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we study two initial value problems arising in general relativity. The first is the Cauchy problem for the linearised Einstein equation on general globally hyperbolic spacetimes, with smooth and distributional initial data. We extend well-known results by showing that given a solution to the linearised constraint equations of arbitrary real Sobolev regularity, there is a globally defined solution, which is unique up to addition of gauge solutions. Two solutions are considered equivalent if they differ by a gauge solution. Our main result is that the equivalence class of solutions depends continuously on the corre- sponding equivalence class of initial data. We also solve the linearised constraint equations in certain cases and show that there exist arbitrarily irregular (non-gauge) solutions to the linearised Einstein equation on Minkowski spacetime and Kasner spacetime. In the second part, we study the Goursat problem (the characteristic Cauchy problem) for wave equations. We specify initial data on a smooth compact...
Download or read book The Einstein Equations and the Large Scale Behavior of Gravitational Fields written by Piotr T. Chrusciel and published by Birkhäuser. This book was released on 2012-12-06 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents state-of-the-art results on the analysis of the Einstein equations and the large scale structure of their solutions. It combines in a unique way introductory chapters and surveys of various aspects of the analysis of the Einstein equations in the large. It discusses applications of the Einstein equations in geometrical studies and the physical interpretation of their solutions. Open problems concerning analytical and numerical aspects of the Einstein equations are pointed out. Background material on techniques in PDE theory, differential geometry, and causal theory is provided.
Download or read book Lectures on Cauchy s Problem in Linear Partial Differential Equations written by Jacques Hadamard and published by . This book was released on 1923 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Cauchy Goursat Problem written by Paul DuChateau and published by American Mathematical Soc.. This book was released on 1972 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Some Aspects of Cauchy s Problem written by Elinar Hille and published by . This book was released on 1954 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on Cauchy s problem in linear partial differential equations written by and published by . This book was released on 1923 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on Cauchy s Problem in Linear Partial Differential Equations written by Jacques Hadamard and published by . This book was released on 1952 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Cauchy Problem written by Sigeru Mizohata and published by Academic Press. This book was released on 2014-05-10 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Notes and Reports in Mathematics in Science and Engineering, Volume 3: On the Cauchy Problem focuses on the processes, methodologies, and mathematical approaches to Cauchy problems. The publication first elaborates on evolution equations, Lax-Mizohata theorem, and Cauchy problems in Gevrey class. Discussions focus on fundamental proposition, proof of theorem 4, Gevrey property in t of solutions, basic facts on pseudo-differential, and proof of theorem 3. The book then takes a look at micro-local analysis in Gevrey class, including proof and consequences of theorem 1. The manuscript examines Schrödinger type equations, as well as general view-points on evolution equations. Numerical representations and analyses are provided in the explanation of these type of equations. The book is a valuable reference for mathematicians and researchers interested in the Cauchy problem.
Download or read book Lectures on Cauchy s Problem in Linear Partial Differential Equations Classic Reprint written by Jacques Hadamard and published by Forgotten Books. This book was released on 2017-09-18 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Lectures on Cauchy's Problem in Linear Partial Differential Equations Picard's researches - which we shall quote in their place - are also essential in several parts of the present work. Such is also the case for Le Roux. 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 Hyperbolic Differential Operators And Related Problems written by Vincenzo Ancona and published by CRC Press. This book was released on 2003-03-06 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting research from more than 30 international authorities, this reference provides a complete arsenal of tools and theorems to analyze systems of hyperbolic partial differential equations. The authors investigate a wide variety of problems in areas such as thermodynamics, electromagnetics, fluid dynamics, differential geometry, and topology. Renewing thought in the field of mathematical physics, Hyperbolic Differential Operators defines the notion of pseudosymmetry for matrix symbols of order zero as well as the notion of time function. Surpassing previously published material on the topic, this text is key for researchers and mathematicians specializing in hyperbolic, Schrödinger, Einstein, and partial differential equations; complex analysis; and mathematical physics.
Download or read book CAUCHY PROBLEM IN GENERAL RELATIVITY written by HANS RINGSTROM. and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Constraint Preserving Boundary Conditions for Hyperbolic Formulations of Einstein s Equations written by Nicolae Tarfulea and published by . This book was released on 2004 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Cauchy Problem written by Hector O. Fattorini and published by . This book was released on 1983 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book CRC Handbook of Lie Group Analysis of Differential Equations written by Nail H. Ibragimov and published by CRC Press. This book was released on 1994-11-28 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 2 offers a unique blend of classical results of Sophus Lie with new, modern developments and numerous applications which span a period of more than 100 years. As a result, this reference is up to date, with the latest information on the group theoretic methods used frequently in mathematical physics and engineering. Volume 2 is divided into three parts. Part A focuses on relevant definitions, main algorithms, group classification schemes for partial differential equations, and multifaceted possibilities offered by Lie group theoretic philosophy. Part B contains the group analysis of a variety of mathematical models for diverse natural phenomena. It tabulates symmetry groups and solutions for linear equations of mathematical physics, classical field theory, viscous and non-Newtonian fluids, boundary layer problems, Earth sciences, elasticity, plasticity, plasma theory (Vlasov-Maxwell equations), and nonlinear optics and acoustics. Part C offers an English translation of Sophus Lie's fundamental paper on the group classification and invariant solutions of linear second-order equations with two independent variables. This will serve as a concise, practical guide to the group analysis of partial differential equations.
Download or read book Technical Abstract Bulletin written by and published by . This book was released on 1967 with total page 848 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Cauchy Problem written by Hector O. Fattorini and published by . This book was released on 1983 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with the Cauchy or initial value problem for linear differential equations. It treats in detail some of the applications of linear space methods to partial differential equations, especially the equations of mathematical physics such as the Maxwell, Schrödinger and Dirac equations. Background material presented in the first chapter makes the book accessible to mathematicians and physicists who are not specialists in this area as well as to graduate students.
Download or read book On Uniqueness in the Large of Solutions of Einstein s Equations strong Cosmic Censorship written by Piotr T. Chruściel and published by . This book was released on 1991 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
