Overview
This work develops the methodology according to which classes of discontinuous functions are used in order to investigate a correctness of boundary-value and initial boundary-value problems for the cases with elliptic, parabolic, pseudoparabolic, hyperbolic, and pseudohyperbolic equations and with elasticity theory equation systems that have nonsmooth solutions, including discontinuous solutions. With the basis of this methodology, the monograph shows a continuous dependence of states, namely, of solutions to the enumerated boundary-value and initial boundary-value problems (including discontinuous states) and a dependence of solution traces on distributed controls and controls at sectors of n-dimensional domain boundaries and at n--1-dimensional function-state discontinuity surfaces (i.e., at mean surfaces of thin inclusions in heterogeneous media). Such an aspect provides the existence of optimal controls for the mentioned systems with J.L. Lions' quadratic cost functionals.
Full Product Details
Author: Ivan V. Sergienko ,
Naum Z. Shor ,
Vasyl S. Deineka
Publisher: Springer-Verlag New York Inc.
Imprint: Springer-Verlag New York Inc.
Edition: Softcover reprint of hardcover 1st ed. 2005
Volume: 75
Dimensions:
Width: 15.50cm
, Height: 2.00cm
, Length: 23.50cm
Weight: 0.611kg
ISBN: 9781441954770
ISBN 10: 1441954775
Pages: 383
Publication Date: 08 December 2010
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: In Print
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Reviews
From the reviews of the first edition: The book is devoted to a special class of linear-quadratic optimal control problems governed by partial differential equations ! . the book gives a clear enough understanding of properties of optimal control problems for the basic cases of nonstandard conjugation conditions (including controls) on the interface between the two domains. (Uldis Raitums, Zentralblatt MATH, Vol. 1080, 2006)
From the reviews of the first edition: ""The book is devoted to a special class of linear-quadratic optimal control problems governed by partial differential equations … . the book gives a clear enough understanding of properties of optimal control problems for the basic cases of nonstandard conjugation conditions (including controls) on the interface between the two domains."" (Uldis Raitums, Zentralblatt MATH, Vol. 1080, 2006)
From the reviews of the first edition: The book is devoted to a special class of linear-quadratic optimal control problems governed by partial differential equations ... . the book gives a clear enough understanding of properties of optimal control problems for the basic cases of nonstandard conjugation conditions (including controls) on the interface between the two domains. (Uldis Raitums, Zentralblatt MATH, Vol. 1080, 2006)
