Partial Differential Equations III: The Cauchy Problem. Qualitative Theory of Partial Differential Equations (Softcover Reprint of the Original 1st 19Paperback - Softcover Reprint of the Original 1st 1991, 13 October 2012

Partial Differential Equations III: The Cauchy Problem. Qualitative Theory of Partial Differential Equations (Softcover Reprint of the Original 1st 19
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Part of Series
Encyclopaedia of Mathematical Sciences
Print Length
197 pages
Language
English
Publisher
Springer
Date Published
13 Oct 2012
ISBN-10
3642634907
ISBN-13
9783642634901

Description

, h In the XIX century, mathematical physics continued to be the main source of new partial differential equations and ofproblems involving them. The study ofLaplace's equation and ofthe wave equation had assumed a more systematic nature. In the beginning of the century, Fourier added the heat equation to the aforementioned two. Marvellous progress in obtaining precise solution repre- sentation formulas is connected with Poisson, who obtained formulas for the solution of the Dirichlet problem in a disc, for the solution of the Cauchy problems for the heat equation, and for the three-dimensional wave equation. The physical setting ofthe problem led to the gradual replacement ofthe search for a general solution by the study of boundary value problems, which arose naturallyfrom the physics ofthe problem. Among these, theCauchy problem was of utmost importance. Only in the context of first order equations, the original quest for general integralsjustified itself. Here again the first steps are connected with the names of D'Alembert and Euler; the theory was being intensively 1h developed all through the XIX century, and was brought to an astounding completeness through the efforts ofHamilton, Jacobi, Frobenius, and E. Cartan. In terms of concrete equations, the studies in general rarely concerned equa- tions of higher than second order, and at most in three variables. Classification 'h ofsecond orderequations was undertaken in the second halfofthe XIX century (by Du Bois-Raymond). An increase in the number of variables was not sanc- tioned by applications, and led to the little understood ultra-hyperbolic case.

Product Details

Book Edition:
Softcover Reprint of the Original 1st 1991
Book Format:
Paperback
Country of Origin:
NL
Date Published:
13 October 2012
Dimensions:
23.39 x 15.6 x 1.14 cm
ISBN-10:
3642634907
ISBN-13:
9783642634901
Language:
English
Location:
Berlin, Heidelberg
Pages:
197
Publisher:
Springer
Weight:
303.91 gm

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