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Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

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Open Access Research Article

Optimal mixed control problem dominating by triple system of parabolic equations

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pp. 145–161Vol. 29Issue 1January 2026DOI: 10.47974/JIM-2252XML
Received:
07 Mar 2025
Published Online:
14 Jan 2026
Article type:
Research Article
Language:
EN
Article no.:
JIM-2252
Pages:
145–161

Abstract

This paper is devoted to study one of the important subject in the branch of applied mathematics, namely the optimal mixed control vector problem (OMCVP) dominating by triple system of parabolic PDEs (for brief TSPE). The Galerkin approach is employed to demonstrate the existence and uniqueness theorem of a triple state vector solution (TSVS) of the weak formulation system (SWF) of the TSPE when the mixed control vector (MCV) is specified. The continuity of the operator between the MCV and its conforming TSVS is established. The demonstration of the existence of an optimal mixed control vector (OMCV) controlling by TSVS is done. The Fréchet derivative (FD) of the objective function (OF) is secured. The derivation of the adjiont triple system (ATS) associated to the TSVS is found. The theorem for necessary optimality conditions for the problem is demonstrated. 

Keywords

Subject Classifications

49Jxx49J2035Exx46N10

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