عنوان
پدید آورنده
موضوع
رده
کتابخانه
محل استقرار
INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
9781461217589
(Number (ISBN
9781461272687
NATIONAL BIBLIOGRAPHY NUMBER
Number
b402807
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
Generalized Characteristics of First Order PDEs
General Material Designation
[Book]
Other Title Information
Applications in Optimal Control and Differential Games /
First Statement of Responsibility
by Arik Melikyan.
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Boston, MA :
Name of Publisher, Distributor, etc.
Imprint: Birkhäuser,
Date of Publication, Distribution, etc.
1998.
CONTENTS NOTE
Text of Note
1 Method of Characteristics in Smooth Problems -- 2 Generalized Solutions and Singular Characteristics of First Order PDEs -- 3 First Order PDEs in Variation Calculus, Optimal Control and Diffrential Games -- 4 Differential Games with Simple Motions on the Manifolds -- 5 Games of Simple Pursuit and Approach on Two-Dimensional Cone -- 6 Smooth Solutions of a PDE with Nonsmooth Hamiltonian -- 7 Shock Waves Related to First Order PDEs -- 8 Singular Surfaces of Nonsmooth Solutions to Multiple Integral Variational Problems -- 9 Appendix.
0
SUMMARY OR ABSTRACT
Text of Note
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.
OTHER EDITION IN ANOTHER MEDIUM
International Standard Book Number
9781461272687
PIECE
Title
Springer eBooks
TOPICAL NAME USED AS SUBJECT
Differential equations, Partial.
Mathematics.
PERSONAL NAME - PRIMARY RESPONSIBILITY
Melikyan, Arik.
CORPORATE BODY NAME - ALTERNATIVE RESPONSIBILITY
SpringerLink (Online service)
ORIGINATING SOURCE
Date of Transaction
20190301082500.0
ELECTRONIC LOCATION AND ACCESS
Electronic name
مطالعه متن کتاب [Book]
Y
