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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…mehr

Produktbeschreibung
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. TOC:Preface.- Control of Systems Described by Elliptic-Type Partial-Differential Equations Under Conjugation Conditions.- Control of a Conditionally Correct System Described by the Neumann Problem for an Elliptic-Type Equation Under Conjugation Conditions.- Control of a System Described by a One-Dimensional Quartic Equation Under Conjugation Conditions.- Control of a System Described by a Two-Dimensional Quartic Equation Under Conjugation Conditions.- Control of a System Described by a Parabolic Equation Under Conjugation Conditions.- Control of a System Described by a Parabolic Equation in the Presence of Concentrated Heat Capacity.- Control of a System Described by a Pseudoparabolic Equation Under Conjugation Conditions.- Control of a System Described by a Hyperbolic Equation Under Conjugation Conditions.- Control of a System Described by a Pseudohyperbolic Equation Under Conjugation Conditions.- Optimal Control of a Deformed Complicated Solid Body State.- References.

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  • Produktdetails
  • Verlag: Springer-Verlag GmbH
  • Erscheinungstermin: 30. März 2006
  • Englisch
  • ISBN-13: 9780387242569
  • Artikelnr.: 37288355
Autorenporträt
Ivan V. Sergienko, V.M. Glushkov Institute of Cybernetics, Kiev, Ukraine / Vasyl S. Deineka, V.M. Glushkov Institute of Cybernetics, Kiev, Ukraine
Inhaltsangabe
Preface.- Control of Systems Described by Elliptic-Type Partial-Differential Equations Under Conjugation Conditions.- Control of a Conditionally Correct System Described by the Neumann Problem for an Elliptic-Type Equation Under Conjugation Conditions.- Control of a System Described by a One-Dimensional Quartic Equation Under Conjugation Conditions.- Control of a System Described by a Two-Dimensional Quartic Equation Under Conjugation Conditions.- Control of a System Described by a Parabolic Equation Under Conjugation Conditions.- Control of a System Described by a Parabolic Equation in the Presence of Concentrated Heat Capacity.- Control of a System Described by a Pseudoparabolic Equation Under Conjugation Conditions.- Control of a System Described by a Hyperbolic Equation Under Conjugation Conditions.- Control of a System Described by a Pseudohyperbolic Equation Under Conjugation Conditions.- Optimal Control of a Deformed Complicated Solid Body State.- References.
Rezensionen
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)