Generalized Solutions of First Order PDEs - The Dynamical Optimization Perspective (Paperback, Softcover reprint of the original 1st ed. 1995)

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:	Springer-Verlag New York
Country of origin:	United States
Series:	Systems & Control: Foundations & Applications
Release date:	June 2013
First published:	1995
Authors:	Andrei I. Subbotin
Dimensions:	235 x 155 x 18mm (L x W x T)
Format:	Paperback
Pages:	314
Edition:	Softcover reprint of the original 1st ed. 1995
ISBN-13:	978-1-4612-6920-5
Categories:	Books > Reference & Interdisciplinary > Communication studies > Information theory > Cybernetics & systems theory Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Calculus of variations Books > Science & Mathematics > Mathematics > Optimization > General Promotions
LSN:	1-4612-6920-2
Barcode:	9781461269205

Is the information for this product incomplete, wrong or inappropriate? Let us know about it.

Does this product have an incorrect or missing image? Send us a new image.

Is this product missing categories? Add more categories.

Review This Product

No reviews yet - be the first to create one!