Partial Differential Equations Iii: The Cauchy Problem. Qualitative Theory of Partial Differential Equations: 32 - Brossura

Egorov, Yu.V.

Brossura

ISBN 10: 3642634907 ISBN 13: 9783642634901

Casa editrice: Springer, 1991

Riassunto

,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.

Su questo libro

Contenuti:

I. The Cauchy Problem.- II. Qualitative Theory of Second Order Linear Partial Differential Equations.- Author Index.

Product Description:

Book by None

Su questa edizione

• Editore: Springer
• Data di pubblicazione: 1991
• ISBN 10: 3642634907
• ISBN 13: 9783642634901
• Rilegatura: Copertina flessibile
• Numero di pagine: 212