Generalized Solutions of First Order PDEs - The Dynamical Optimization Perspective (Hardcover, 1995 ed.)

Hamilton-Jacobi equations and other types of partial differential equa- tions of the first order are dealt with in many branches of mathematics, mechanics, and physics. These equations are usually nonlinear, and func- tions vital for the considered problems are not smooth enough to satisfy these equations in the classical sense. An example of such a situation can be provided by the value function of a differential game or an optimal control problem. It is known that at the points of differentiability this function satisfies the corresponding Hamilton-Jacobi-Isaacs-Bellman equation. On the other hand, it is well known that the value function is as a rule not everywhere differentiable and therefore is not a classical global solution. Thus in this case, as in many others where first-order PDE's are used, there arises necessity to introduce a notion of generalized solution and to develop theory and methods for constructing these solutions. In the 50s-70s, problems that involve nonsmooth solutions of first- order PDE's were considered by Bakhvalov, Evans, Fleming, Gel'fand, Godunov, Hopf, Kuznetzov, Ladyzhenskaya, Lax, Oleinik, Rozhdestven- ski1, Samarskii, Tikhonov, and other mathematicians. Among the inves- tigations of this period we should mention the results of S.N. Kruzhkov, which were obtained for Hamilton-Jacobi equation with convex Hamilto- nian. A review of the investigations of this period is beyond the limits of the present book. A sufficiently complete bibliography can be found in [58, 126, 128, 141].

General

Imprint:	Birkhauser Boston
Country of origin:	United States
Series:	Systems & Control: Foundations & Applications
Release date:	December 1994
First published:	1995
Authors:	Andrei I. Subbotin
Dimensions:	235 x 155 x 19mm (L x W x T)
Format:	Hardcover
Pages:	314
Edition:	1995 ed.
ISBN-13:	978-0-8176-3740-8
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations Promotions
LSN:	0-8176-3740-0
Barcode:	9780817637408

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