000			03914nmm a22002175i 4500
005			20230705150630.0
008			121227s1978 xxu| s |||| 0|eng d
020			_a9781468400595 _9978-1-4684-0059-5
082			_a515.35 _223
100			_aJohn, F. _920085
245			_aPartial Differential Equations _h[electronic resource] / _cby F. John.
250			_a3rd ed. 1978.
260			_aNew York, NY : _bSpringer New York : _bImprint: Springer, _c1978.
300			_bonline resource.
505			_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			_aDifferential equations. _920086
650			_aDifferential Equations. _920087
856			_uhttps://doi.org/10.1007/978-1-4684-0059-5
942			_cEBK
999			_c13601 _d13601