Generalized Solutions of First Order PDEs: The Dynamical Optimization Perspective (Systems & Control: Foundations & Applications).

Subbotin, Andrei I.:

ISBN 10: 0817637400 / ISBN 13: 9780817637408

Editore: Boston: Birkhäuser, 1995

Riguardo questo articolo

Zust: Gutes Exemplar. Buchblock invers zu Einband. XI, 326 Seiten Englisch 636g.

Codice articolo 492972

Dati bibliografici

• Titolo: Generalized Solutions of First Order PDEs: The Dynamical Optimization Perspective (Systems & Control: Foundations & Applications).
• Editore: Boston: Birkhäuser
• Data di pubblicazione: 1995
• Lingua: Inglese
• ISBN 10: 0817637400
• ISBN 13: 9780817637408
• Rilegatura: gebundene Ausgabe
• Condizione: Gut
• Peso: 636 grammi
• Cataloghi dei venditori:
  • Mathematik

Descrizione articolo

Riassunto

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].

Recensione

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