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 Cauchy Goursat Problem written by Paul DuChateau and published by . This book was released on 1972 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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:
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 0 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 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 The Cauchy Goursat Theorem and Its Applications written by Melvin Cleo Withnell and published by . This book was released on 1958 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Cauchy Problem written by Hector O. Fattorini and published by Cambridge University Press. This book was released on 1983 with total page 664 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 Generalized Goursat Problem for a Hyperbolic System written by Robert Peter Holten and published by . This book was released on 1958 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Mixed and Cauchy Goursat Problems in Several Time Variables written by Alexander Brenner and published by . This book was released on 1999 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Partial Differential Equations in Classical Mathematical Physics written by Isaak Rubinstein and published by Cambridge University Press. This book was released on 1998-04-28 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: The unique feature of this book is that it considers the theory of partial differential equations in mathematical physics as the language of continuous processes, that is, as an interdisciplinary science that treats the hierarchy of mathematical phenomena as reflections of their physical counterparts. Special attention is drawn to tracing the development of these mathematical phenomena in different natural sciences, with examples drawn from continuum mechanics, electrodynamics, transport phenomena, thermodynamics, and chemical kinetics. At the same time, the authors trace the interrelation between the different types of problems - elliptic, parabolic, and hyperbolic - as the mathematical counterparts of stationary and evolutionary processes. This combination of mathematical comprehensiveness and natural scientific motivation represents a step forward in the presentation of the classical theory of PDEs, one that will be appreciated by both students and researchers alike.
Download or read book Cauchy Goursat Problem for Hyper Quasilinear Hyperbolic Systems written by Duplex Elvis Houpa Danga and published by . This book was released on 2018 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: Smoothness results are estalished for hyper quasilinear systems of second order with data on two intersecting null hypersurfaces.Problème de Cauchy-Goursat pour des systèmes hyper quasi-linéaires hyperboliquesRésumé Des résultats de régularité sont établis pour des systèmes hyper quasi-linéaires hyperboliques du second ordre à données sur deux hypersurfaces caractéristiques sécantes.
Download or read book Lectures on Cauchy s Problem in Linear Partial Differential Equations written by Jacques Hadamard and published by Courier Corporation. This book was released on 2014-08-25 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Would well repay study by most theoretical physicists." — Physics Today "An overwhelming influence on subsequent work on the wave equation." — Science Progress "One of the classical treatises on hyperbolic equations." — Royal Naval Scientific Service Delivered at Columbia University and the Universities of Rome and Zürich, these lectures represent a pioneering investigation. Jacques Hadamard based his research on prior studies by Riemann, Kirchhoff, and Volterra. He extended and improved Volterra's work, applying its theories relating to spherical and cylindrical waves to all normal hyperbolic equations instead of only to one. Topics include the general properties of Cauchy's problem, the fundamental formula and the elementary solution, equations with an odd number of independent variables, and equations with an even number of independent variables and the method of descent.
Download or read book STABILITY AND CONVERGENCE FOR A NUMERICAL SOLUTION OF THE GOURSAT PROBLEM written by RALPH THEODORE DAMES and published by . This book was released on 1957 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Student Study Guide to Accompany A First Course in Complex Analysis with Applications written by Shanahan and published by Jones & Bartlett Publishers. This book was released on 2009-09-29 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Student Study Guide to Accompany A First Course in Complex Analysis, Second Edition is designed to help you get the most out of your Complex Analysis course. It includes chapter-by-chapter, and section-by-section, detailed summaries of key points and terms found within the main text. Review Sections form selected topics in calculus and differential equations allow you to confirm your understanding of the prerequisite material necessary to succeed in the course. Complete worked solutions, with two-color figures, are provided form every other odd exercise and include references to equations, definitions, theorems, and figures in the text. This useful learning tool engages you to assess your progress and understanding while encouraging you to find solutions on your own. Students, Use This Guide To: - Review and confirm your understanding of prerequisite material. - Revisit key points and terms discussed within each chapter. - Check answers to selected exercises - Prepare for future material
Download or read book Approximation Methods for Solutions of Differential and Integral Equations written by V. K. Dzyadyk and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-11-05 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Approximation Methods for Solutions of Differential and Integral Equations".
Download or read book Space Time Matter written by Jochen Brüning and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-04-09 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph describes some of the most interesting results obtained by the mathematicians and physicists collaborating in the CRC 647 "Space – Time – Matter", in the years 2005 - 2016. The work presented concerns the mathematical and physical foundations of string and quantum field theory as well as cosmology. Important topics are the spaces and metrics modelling the geometry of matter, and the evolution of these geometries. The partial differential equations governing such structures and their singularities, special solutions and stability properties are discussed in detail. Contents Introduction Algebraic K-theory, assembly maps, controlled algebra, and trace methods Lorentzian manifolds with special holonomy – Constructions and global properties Contributions to the spectral geometry of locally homogeneous spaces On conformally covariant differential operators and spectral theory of the holographic Laplacian Moduli and deformations Vector bundles in algebraic geometry and mathematical physics Dyson–Schwinger equations: Fix-point equations for quantum fields Hidden structure in the form factors ofN = 4 SYM On regulating the AdS superstring Constraints on CFT observables from the bootstrap program Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities Yangian symmetry in maximally supersymmetric Yang-Mills theory Wave and Dirac equations on manifolds Geometric analysis on singular spaces Singularities and long-time behavior in nonlinear evolution equations and general relativity
Download or read book Multidimensional Analysis and Discrete Models written by Aleksei A. Dezin and published by CRC Press. This book was released on 2018-01-18 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multidimensional Analysis and Discrete Models, a thorough and detailed reference, covers the main structures of multidimensional analysis and the intrinsically defined discrete models in applied mathematics, mathematical physics, and related fields. The material is presented in a clear and straightforward manner, with background information provided to define finite models and to clarify the concepts of multidimensional analysis. The book covers special difference models of the mathematical physics equations, models of boundary value problems, and objects of quantum mechanics. Considerable attention is also given to differential operators on Riemannian manifolds and the interpretation of classical vector analysis. The primary focus of Multidimensional Analysis and Discrete Models is on the description of regular methods of constructing intrinsically defined discrete models for special classes of continual objects, but emphasis is also given to the interaction of ideas and methods that exist throughout the field of mathematics. For example, the connections between theories derived from classical and functional analysis, Riemannian geometry, and algebraic topology are illustrated, and are discussed in terms of their relevance to computing solutions.
