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Titlebook: Partial Differential Equations; Fritz John Textbook 19783rd edition Springer-Verlag New York Inc. 1978 Cauchy problem.Equations.Finite.Fou

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书目名称Partial Differential Equations
编辑Fritz John
视频video
丛书名称Applied Mathematical Sciences
图书封面Titlebook: Partial Differential Equations;  Fritz John Textbook 19783rd edition Springer-Verlag New York Inc. 1978 Cauchy problem.Equations.Finite.Fou
描述The book has been completely rewritten for this new edition. While most of the material found in the earlier editions has been retained, though in changed form, there are considerable additions, in which extensive use is made of Fourier transform techniques, Hilbert space, and finite difference methods. A condensed version of the present work was presented in a series of lectures as part of the Tata Institute of Fundamental Research -Indian Insti­ tute of Science Mathematics Programme in Bangalore in 1977. I am indebted to Professor K. G. Ramanathan for the opportunity to participate in this excit­ ing educational venture, and to Professor K. Balagangadharan for his ever ready help and advice and many stimulating discussions. Very special thanks are due to N. Sivaramakrishnan and R. Mythili, who ably and cheerfully prepared notes of my lectures which I was able to use as the nucleus of the present edition. A word about the choice of material. The constraints imposed by a partial differential equation on its solutions (like those imposed by the environment on a living organism) have an infinite variety of con­ sequences, local and global, identities and inequalities. Theories of suc
出版日期Textbook 19783rd edition
关键词Cauchy problem; Equations; Finite; Fourier transform; Partielle Differentialgleichung; constraint; differe
版次3
doihttps://doi.org/10.1007/978-1-4684-0059-5
isbn_softcover978-1-4684-0061-8
isbn_ebook978-1-4684-0059-5Series ISSN 0066-5452 Series E-ISSN 2196-968X
issn_series 0066-5452
copyrightSpringer-Verlag New York Inc. 1978
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978-1-4684-0061-8Springer-Verlag New York Inc. 1978
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Hyperbolic equations in higher dimensions,erator “□” defined by (1.1) is known as the .. For .=3 the equation can represent waves in acoustics or optics, for .=2 waves on the surface of water, for .=1 sound waves in pipes or vibrations of strings. In the initial-value problem we ask for a solution of (1.1) defined in the (.+1)-dimensional half space .>0 for which
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Higher-order elliptic equations with constant coefficients,lves to a single linear homogeneous .th-order equation with constant real coefficients for a scalar function .(.)=.(.,...,.). We write the equation in the familiar form . where . is an .th-degree form in .=(.,...,.) with constant real coefficients .. Equation (0.1) is . (see p. 58), if there are no real characteristic surfaces, that is, if
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Parabolic equations,erature in a heat-conducting medium. For .=1 it holds for the temperature distribution in a heat-conducting insulated wire. The same type of equation occurs in the description of diffusion processes. Applying a suitable linear substitution on . we transform (1.1) into . which will be used in the discussion to follow.
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The Laplace equation,The . acting on a function .(.) = .(.,...,.) of class . in a region Ω is defined by . For . we have (see Chapter 3, (4.8), (4.9)) Green’s identities. . where . indicates differentiation in the direction of . normal to ∂Ω.
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