Fr. 134.00

Generalized Solutions of First Order PDEs - The Dynamical Optimization Perspective

Inglese · Copertina rigida

Spedizione di solito entro 2 a 3 settimane (il titolo viene stampato sull'ordine)

Descrizione

Ulteriori informazioni

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].

Sommario

I Generalized Characteristics of First-Order PDE's.- II Cauchy Problems for Hamilton-Jacobi Equations.- III Differential Games.- IV Boundary-Value Problems for First-Order PDE's.- A1 Justification of the Classical Method of Characteristics.- A2 Multifunctions.- A3 Semicontinuous Functions.- A4 Convex Functions.- A5 Contingent Tangent Cones, Directional Derivatives, Subdifferentials.- A6 On a Property of Subdifferentials.- A7 Differential Inclusions.- A8 Criteria for Weak Invariance.

Relazione

"Subbotin's book is a very valuable addition to the literature."
- Mathematical Reviews
"The book is printed excellently and clearly. The explanations concerning the content are distinguished of high correctness and equipped with numerous examples and illustrations."
- ZAA

Dettagli sul prodotto

Autori Andrei I Subbotin, Andrei I. Subbotin
Editore Springer, Basel
 
Lingue Inglese
Formato Copertina rigida
Pubblicazione 26.06.2009
 
EAN 9780817637408
ISBN 978-0-8176-3740-8
Pagine 314
Dimensioni 155 mm x 21 mm x 235 mm
Peso 660 g
Illustrazioni XII, 314 p.
Serie Systems & Control: Foundations & Applications
Systems & Control: Foundations & Applications
Categoria Scienze naturali, medicina, informatica, tecnica > Matematica > Analisi

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