Description: Generalized Characteristics of First Order Pdes : Applications in Optimal Control and Differntial Games, Hardcover by Melikyan, A. A., ISBN 0817639845, ISBN-13 9780817639846, Brand New, Free shipping in the US In some domains of mechanics, physics and control theory boundary value problems arise for nonlinear first order PDEs. A well-known classical result states a sufficiency condition for local existence and uniqueness of twice differentiable solution. This result is based on the method of characteristics (MC). Very often, and as a rule in control theory, the continuous nonsmooth (non-differentiable) functions have to be treated as a solutions to the PDE. At the points of smoothness such solutions satisfy the equation in classical sense. But if a function satisfies this condition only, with no requirements at the points of nonsmoothness, the PDE may have nonunique solutions. The uniqueness takes place if an appropriate matching principle for smooth solution branches defined in neighboring domains is applied or, in other words, the notion of generalized solution is considered. In each field an appropriate matching principle are used. In Optimal Control and Differential Games this principle is the optimality of the cost function. In physics and mechanics certain laws must be fulfilled for correct matching. A purely mathematical approach also can be used, when the generalized solution is introduced to obtain the existence and uniqueness of the solution, without being aimed to describe (to model) some particular physical phenomenon. Some formulations of the generalized solution may meet the modelling of a given phenomenon, the others may not.
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Book Title: Generalized Characteristics of First Order Pdes : Applications in
Number of Pages: Xiv, 310 Pages
Publication Name: Generalized Characteristics of First Order PDEs : Applications in Optimal Control and Differential Games
Language: English
Publisher: Birkhäuser Boston
Subject: Game Theory, Differential Equations / General, Mechanics / Dynamics, Differential Equations / Partial
Publication Year: 1998
Type: Textbook
Item Weight: 50.1 Oz
Subject Area: Mathematics, Science
Item Length: 9.3 in
Author: Arik Melikyan
Item Width: 6.1 in
Format: Hardcover
