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eBook Partial Differential Equations II: Elements of the Modern Theory. Equations with Constant Coefficients (Encyclopaedia of Mathematical Sciences) (v. 2) ePub

eBook Partial Differential Equations II: Elements of the Modern Theory. Equations with Constant Coefficients (Encyclopaedia of Mathematical Sciences) (v. 2) ePub

by Yu.V. Egorov,A.I. Komech,M.A. Shubin,P.C. Sinha

  • ISBN: 3540520015
  • Category: Mathematics
  • Subcategory: Math Science
  • Author: Yu.V. Egorov,A.I. Komech,M.A. Shubin,P.C. Sinha
  • Language: English
  • Publisher: Springer; 1994 edition (December 19, 1994)
  • Pages: 266
  • ePub book: 1158 kb
  • Fb2 book: 1207 kb
  • Other: lit doc mobi mbr
  • Rating: 4.7
  • Votes: 126

Description

Sinha (Translator) & 1 more Summarizing, the book presents a well-written survey of the modern theory of general PDE-s with most necessary proofs or hints, and with some explicit.

Sinha (Translator) & 1 more. Therefore it will be useful for specialists in PDE-s as well as for students with basic knowledge in classical theory of PDE-s. The book is warmly recommended also to physicists, engineers and anyone interested in theory or/and applications of PDE-s. J. Hegedüs, Acta Scientiarum Mathematicarum, Vol. 70, 2004.

Equations with Constant Coefficients. Authors: Egorov, Y.

Электронная книга "Partial Differential Equations II: Elements of the Modern Theory. Equations with Constant Coefficients", Y. Эту книгу можно прочитать в Google Play Книгах на компьютере, а также на устройствах Android и iOS. Выделяйте текст, добавляйте закладки и делайте заметки, скачав книгу "Partial Differential Equations II: Elements of the Modern Theory. Equations with Constant Coefficients" для чтения в офлайн-режиме.

a welcome addition to the literature. It is comparable in scope with the great Courant-Hilbert Methods of Mathematical Physics, but it is much shorter, more up to date of course, and contains more elaborate analytical machinery. The Mathematical Gazette, 1993.

equation with variable coefficients from the PDE with constant coefficients, however the most. of the partial differential equations with variable coefficients depend on nature of particular. In the next we use the convolution technique to generate a PDE. with variable coefficients by using the equation (25) and compare the solution with the solu-. tion of the equation (25).

are some constant coefficients. For each of the equation we can write the so-called characteristic (auxiliary) equation: k2+pk+q 0. The general solution of the homogeneous differential equation depends on the roots of the characteristic quadratic equation. There are the following options: Discriminant of the characteristic quadratic equation D 0. Then the roots of the characteristic equations k1. and k2. are real and distinct. In this case the general solution is given by the following function. y(x) C1ek1x+C2ek2x, where C1. and C2. are arbitrary real numbers.

In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a computer model. A special case is ordinary differential equations (ODEs), which deal with functions of a single variable and their derivatives.

Raevskii, Some properties of the potential theory operators and and their application to investigation of the basic . A. Shlapunov, A Method for Constructing Solutions to Linear Systems of Partial Differential Equations, Siberian Adv. Math. 17:2 (2007), 144–152.

Raevskii, Some properties of the potential theory operators and and their application to investigation of the basic electro- and magnetostatic equation, Theoret. 100:3 (1994), 1040–1045. E. K. Lipachev, Kraevye zadachi Dirikhle i Neimana dlya uravneniya Gelmgoltsa v neogranichennykh oblastyakh s kusochno-gladkim uchastkom granitsy, Uchen. nauki, 148, no. 3, Izd-vo Kazanskogo un-ta, Kazan, 2006, 94–108.

This book, the first printing of which was published as Volume 31 of the Encyclopaedia of Mathematical Sciences, contains a survey of the modern theory of general linear partial differential equations and a detailed review of equations with constant coefficients. Readers will be interested in an introduction to microlocal analysis and its applications including singular integral operators, pseudodifferential operators, Fourier integral operators and wavefronts, a survey of the most important results about the mixed problem for hyperbolic equations, a review of asymptotic methods including short wave asymptotics, the Maslov canonical operator and spectral asymptotics, a detailed description of the applications of distribution theory to partial differential equations with constant coefficients including numerous interesting special topics.

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