9780817637408 - Generalized Solutions of First Order PDEs: The Dynamical Optimization Perspective di Subbotin, Andrei I. (24 risultati)

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Hardcover. Condizione: new. Hardcover. Hamilton-Jacobi equations and other types of partial differential equations of the first order are dealt with in many branches of mathematics, mechanics and physics. As a rule, functions vital for the considered problems are not smooth enough to satisfy these equations in the classical sense. Thus, there arises the need to introduce a notion of a generalized solution and to develop theory and methods for constructing these solutions. This text presents an approach to partial differential equations that can be considered as a non-classical method of characteristics, according to which the generalized solution (the minimax solution) is assumed to be flow invariant with respect to the so-called characteristic inclusions. The research on minimax solutions employs methods of the theory of differential games, dynamical optimization and nonsmooth analysis. At the same time, this research has contributed to the development of these new branches of mathematics. The book is intended as a self-contained exposition of the theory of minimax solutions. It includes existence and uniqueness results, examples of modelling and applications to the theory of control and differential games. This text presents an approach to partial differential equations that can be considered as a non-classical method of characteristics, according to which the generalized solution (the minimax solution) is assumed to be flow invariant with respect to the so-called characteristic inclusions. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

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Condizione: New. 1994. Hardcover. . . . . .

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Buch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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].

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Hardcover. Condizione: new. Hardcover. Hamilton-Jacobi equations and other types of partial differential equations of the first order are dealt with in many branches of mathematics, mechanics and physics. As a rule, functions vital for the considered problems are not smooth enough to satisfy these equations in the classical sense. Thus, there arises the need to introduce a notion of a generalized solution and to develop theory and methods for constructing these solutions. This text presents an approach to partial differential equations that can be considered as a non-classical method of characteristics, according to which the generalized solution (the minimax solution) is assumed to be flow invariant with respect to the so-called characteristic inclusions. The research on minimax solutions employs methods of the theory of differential games, dynamical optimization and nonsmooth analysis. At the same time, this research has contributed to the development of these new branches of mathematics. The book is intended as a self-contained exposition of the theory of minimax solutions. It includes existence and uniqueness results, examples of modelling and applications to the theory of control and differential games. This text presents an approach to partial differential equations that can be considered as a non-classical method of characteristics, according to which the generalized solution (the minimax solution) is assumed to be flow invariant with respect to the so-called characteristic inclusions. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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]. 330 pp. Englisch.

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Buch. Condizione: Neu. Generalized Solutions of First Order PDEs | The Dynamical Optimization Perspective | Andrei I. Subbotin | Buch | xii | Englisch | 1994 | Birkhäuser Boston | EAN 9780817637408 | Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu Print on Demand.

Buch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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].Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 330 pp. Englisch.