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" Hyperbolic partial differential equations and wave phenomena / "
Mitsuru Ikawa ; translated by Bohdan I. Kurpita.
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BL
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| Record Number
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637095
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| Doc. No
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dltt
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| Uniform Title
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Henbibun hōteishiki 2.English
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| Main Entry
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Ikawa, Mitsuru,1942-
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| Title & Author
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Hyperbolic partial differential equations and wave phenomena /\ Mitsuru Ikawa ; translated by Bohdan I. Kurpita.
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| Publication Statement
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Providence, RI :: American Mathematical Society,, c2000.
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| Series Statement
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Iwanami series in modern mathematics
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Translations of mathematical monographs ;; v. 189
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| Page. NO
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xxi, 190 p. ;; 22 cm.
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| ISBN
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0821810219 (alk. paper)
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: 9780821810217 (alk. paper)
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| Bibliographies/Indexes
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Includes bibliographical references (p. 179-180) and index.
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| Contents
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Wave Phenomena and Hyperbolic Equations -- Equations of wave phenomena -- The vibration of a string -- The equation of oscillation of a spring -- The equation for the propagation of sound -- Maxwell's equations, elastic equations -- Hyperbolic partial differential operators -- Hyperbolic differential operators -- Problems that we will consider -- Formulae for solutions of an initial value problem for a wave equation -- The Existence of a Solution for a Hyperbolic Equation and its Properties -- Finite propagation speed, domains of dependence and influence -- Energy estimate of the solution -- The domain of dependence -- The domain of influence -- Finite speed of propagation -- An a priori estimate of the solution -- On the premise of results for elliptic equations -- Energy estimate -- An estimate of partial derivatives of higher order -- Elimination of the extra assumption, approximation due a mollifier -- Energy conservation -- Existence of the solution -- The Hille-Yosida theorem -- The operator A -- The existence of a solution for the initial boundary value problem -- Smoothness of the solution -- The Construction of Asymptotic Solutions -- An asymptotic solution of the hyperbolic equation -- The Eikonal equation -- Canonical equations -- The construction of the solution -- The transport equation and the behaviour of the asymptotic solution -- The transport equation -- The behaviour of the asymptotic solution -- The propagation of sound in air in which the temperature is not constant -- The propagation of singularities.
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| Subject
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Differential equations, Hyperbolic.
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Boundary value problems.
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Wave equation.
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| LC Classification
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QA377.I4713 2000
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