Generalized Characteristics of First Order PDEs

Language: English

Published by Birkhäuser, Birkhäuser Mai 1998, 1998

0817639845 / 9780817639846

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This item is printed on demand - Print on Demand Titel. Neuware -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.Springer Nature c/o IBS, Benzstrasse 21, 48619 Heek 332 pp. Englisch.…

Seller Inventory # 9780817639846

Title
Generalized Characteristics of First Order PDEs
Author
Arik Melikyan
Publisher
Birkhäuser, Birkhäuser Mai 1998
Publication year
1998
Condition
Neu
Binding
Buch
Language
English
ISBN 10
0817639845
ISBN 13
9780817639846
Item weight
664 grams
Dimensions
241x160x23 mm

buchversandmimpf2000

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