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020 _a9781468400595
_9978-1-4684-0059-5
024 7 _a10.1007/978-1-4684-0059-5
_2doi
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
072 7 _aPBKJ
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082 0 4 _a515.35
_223
100 1 _aJohn, F.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_966628
245 1 0 _aPartial Differential Equations
_h[electronic resource] /
_cby F. John.
250 _a3rd ed. 1978.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c1978.
300 _bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aApplied Mathematical Sciences,
_x2196-968X ;
_v1
505 0 _a1 The single first-order equation -- 1. Introduction -- 2. Examples -- 3. Analytic Solution and Approximation Methods in a Simple Example -- 4. Quasi-linear Equations -- 5. The Cauchy Problem for the Quasi-linear Equation -- 6. Examples -- 7. The General First-order Equation for a Function of Two Variables -- 8. The Cauchy Problem -- 9. Solutions Generated as Envelopes -- 2 Second-order equations: hyperbolic equations for functions of two independent variables -- 1. Characteristics for Linear and Quasi-linear Second-order Equations -- 2. Propagation of Singularities -- 3. The Linear Second-order Equation -- 4. The One-Dimensional Wave Equation -- 5. Systems of First-order Equations (Courant-Lax Theory) -- 6. A Quasi-linear System and Simple Waves -- 3 Characteristic manifolds and the Cauchy problem -- 1. Notation of Laurent Schwartz -- 2. The Cauchy Problem -- 3. Cauchy-Kowalewski Theorem -- 4. The Lagrange-Green Identity -- 5. The Uniqueness Theorem of Holmgren -- 6. Distribution Solutions -- 4 The Laplace equation -- 1. Green’s Identity, Fundamental Solutions -- 2. The Maximum Principle -- 3. The Dirichlet Problem, Green’s Function, and Poisson’s Formula -- 4. Proof of Existence of Solutions for the Dirichlet Problem Using Subharmonic Functions (“Perron’s Method”) -- 5. Solution of the Dirichlet Problem by Hilbert-Space Methods -- 5 Hyperbolic equations in higher dimensions -- 1. The Wave Equation in n-dimensional Space -- 2. Higher-order Hyperbolic Equations with Constant Coefficients -- 3. Symmetric Hyperbolic Systems -- 6 Higher-order elliptic equations with constant coefficients -- 1. The Fundamental Solution for Odd n -- 2. The Dirichlet Problem -- 7 Parabolic equations -- 1. The Heat Equation -- 2. The Initial-value Problem for General Second-order Linear Parabolic Equations.
520 _aThe 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 such equations usually attempt to analyse the structure of individual solutions and of the whole manifold of solutions by testing the compatibility of the differential equation with various types of additional constraints.
650 0 _aDifferential equations.
_966629
650 1 4 _aDifferential Equations.
_966630
710 2 _aSpringerLink (Online service)
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773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
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776 0 8 _iPrinted edition:
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776 0 8 _iPrinted edition:
_z9781468400601
830 0 _aApplied Mathematical Sciences,
_x2196-968X ;
_v1
_966632
856 4 0 _uhttps://doi.org/10.1007/978-1-4684-0059-5
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