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Partial Differential Equations Of Mathematical Physics

Author: S. L. Sobolev
Publisher: Elsevier
ISBN: 1483181367
Size: 29.79 MB
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Pure and Applied Mathematics, Volume 56: Partial Differential Equations of Mathematical Physics provides a collection of lectures related to the partial differentiation of mathematical physics. This book covers a variety of topics, including waves, heat conduction, hydrodynamics, and other physical problems. Comprised of 30 lectures, this book begins with an overview of the theory of the equations of mathematical physics that has its object the study of the integral, differential, and functional equations describing various natural phenomena. This text then examines the linear equations of the second order with real coefficients. Other lectures consider the Lebesgue-Fubini theorem on the possibility of changing the order of integration in a multiple integral. This book discusses as well the Dirichlet problem and the Neumann problem for domains other than a sphere or half-space. The final lecture deals with the properties of spherical functions. This book is a valuable resource for mathematicians.

Partial Differential Equations In Physics

Publisher: Academic Press
ISBN: 9780080873091
Size: 40.10 MB
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The topic with which I regularly conclude my six-term series of lectures in Munich is the partial differential equations of physics. We do not really deal with mathematical physics, but with physical mathematics; not with the mathematical formulation of physical facts, but with the physical motivation of mathematical methods. The oftmentioned “prestabilized harmony between what is mathematically interesting and what is physically important is met at each step and lends an esthetic - I should like to say metaphysical -- attraction to our subject. The problems to be treated belong mainly to the classical matherhatical literature, as shown by their connection with the names of Laplace, Fourier, Green, Gauss, Riemann, and William Thomson. In order to show that these methods are adequate to deal with actual problems, we treat the propagation of radio waves in some detail in Chapter VI.

Boundary Value Problems For Linear Evolution Partial Differential Equations

Author: H.G. Garnir
Publisher: Springer Science & Business Media
ISBN: 9401012059
Size: 50.94 MB
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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,,

Trends In Partial Differential Equations Of Mathematical Physics

Author: José F. Rodrigues
Publisher: Springer Science & Business Media
ISBN: 3764373172
Size: 30.93 MB
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This book consists of contributions originating from a conference in Obedo, Portugal, which honoured the 70th birthday of V.A. Solonnikov. A broad variety of topics centering on nonlinear problems is presented, particularly Navier-Stokes equations, viscosity problems, diffusion-absorption equations, free boundaries, and Euler equations.

Fourier Analysis And Nonlinear Partial Differential Equations

Author: Hajer Bahouri
Publisher: Springer Science & Business Media
ISBN: 9783642168307
Size: 30.91 MB
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In recent years, the Fourier analysis methods have expereinced a growing interest in the study of partial differential equations. In particular, those techniques based on the Littlewood-Paley decomposition have proved to be very efficient for the study of evolution equations. The present book aims at presenting self-contained, state- of- the- art models of those techniques with applications to different classes of partial differential equations: transport, heat, wave and Schrödinger equations. It also offers more sophisticated models originating from fluid mechanics (in particular the incompressible and compressible Navier-Stokes equations) or general relativity. It is either directed to anyone with a good undergraduate level of knowledge in analysis or useful for experts who are eager to know the benefit that one might gain from Fourier analysis when dealing with nonlinear partial differential equations.

Partial Differential Equations In Clifford Analysis

Author: Elena Obolashvili
Publisher: CRC Press
ISBN: 9780582317499
Size: 72.45 MB
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Clifford analysis represents one of the most remarkable fields of modern mathematics. With the recent finding that almost all classical linear partial differential equations of mathematical physics can be set in the context of Clifford analysis-and that they can be obtained without applying any physical laws-it appears that Clifford analysis itself can suggest new equations or new generalizations of classical equations that may have some physical content. Partial Differential Equations in Clifford Analysis considers-in a multidimensional space-elliptic, hyperbolic, and parabolic operators related to Helmholtz, Klein-Gordon, Maxwell, Dirac, and heat equations. The author addresses two kinds of parabolic operators, both related to the second-order parabolic equations whose principal parts are the Laplacian and d'Alembertian: an elliptic-type parabolic operator and a hyperbolic-type parabolic operator. She obtains explicit integral representations of solutions to various boundary and initial value problems and their properties and solves some two-dimensional and non-local problems. Written for the specialist but accessible to non-specialists as well, Partial Differential Equations in Clifford Analysis presents new results, reformulations, refinements, and extensions of familiar material in a manner that allows the reader to feel and touch every formula and problem. Mathematicians and physicists interested in boundary and initial value problems, partial differential equations, and Clifford analysis will find this monograph a refreshing and insightful study that helps fill a void in the literature and in our knowledge.

Partial Differential Equations Of First Order And Their Applications To Physics

Author: Gustavo López Velázquez
Publisher: World Scientific Publishing Company
ISBN: 9814397504
Size: 37.38 MB
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This book tries to point out the mathematical importance of the Partial Differential Equations of First Order (PDEFO) in Physics and Applied Sciences. The intention is to provide mathematicians with a wide view of the applications of this branch in physics, and to give physicists and applied scientists a powerful tool for solving some problems appearing in Classical Mechanics, Quantum Mechanics, Optics, and General Relativity. This book is intended for senior or first year graduate students in mathematics, physics, or engineering curricula. This book is unique in the sense that it covers the applications of PDEFO in several branches of applied mathematics, and fills the theoretical gap between the formal mathematical presentation of the theory and the pure applied tool to physical problems that are contained in other books. Improvements made in this second edition include corrected typographical errors; rewritten text to improve the flow and enrich the material; added exercises in all chapters; new applications in Chapters 1, 2, and 5 and expanded examples. Contents:Geometric Concepts and GeneralitiesPartial Differential Equations of First OrderPhysical Applications INonlinear Partial Differential Equations of First OrderPhysical Applications IICharacteristic Surfaces of Linear Partial Differential Equation of Second Order Readership: Mathematicians, physicists, applied scientists, senior or first year graduate students in mathematics, physics or engineering.