Generalized Characteristics of First Order PDEs | Applications in Optimal Control and Differential Games

Arik Melikyan

ISBN 10: 1461272688 / ISBN 13: 9781461272687

Published by Birkhäuser, 2012

About this Item

Generalized Characteristics of First Order PDEs | Applications in Optimal Control and Differential Games | Arik Melikyan | Taschenbuch | xiv | Englisch | 2012 | Birkhäuser | EAN 9781461272687 | 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.

Seller Inventory # 106029421

Bibliographic Details

• Title: Generalized Characteristics of First Order PDEs | Applications in Optimal Control and Differential Games
• Publisher: Birkhäuser
• Publication Date: 2012
• Language: English
• ISBN 10: 1461272688
• ISBN 13: 9781461272687
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 18D millimeters 235 millimeters width by 155 millimeters height by 18 millimeters depth
• Weight: 499 grams
• Seller catalogs:
  • Bücher

About this title

Synopsis

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.