On the time-optimal control problem for a fourth order parabolic equation in a two-dimensional domain

Autor:	Ф.Н. Дехконов
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	initial-boundary problem fourth-order parabolic equation minimal time admissible control Volterra integral equation Laplace transform method Analysis QA299.6-433 Analytic mechanics QA801-939 Probabilities. Mathematical statistics QA273-280
Zdroj:	Қарағанды университетінің хабаршысы. Математика сериясы, Vol 114, Iss 2 (2024)
Druh dokumentu:	article
ISSN:	2518-7929 2663-5011
DOI:	10.31489/2024m2/57-70
Popis:	Previously, boundary control problems for the second order parabolic type equation in the bounded domain were studied. In this paper, a boundary control problem associated with a fourth-order parabolic equation in a bounded two-dimensional domain was considered. On the part of the considered domain’s boundary, the value of the solution with control function is given. Restrictions on the control are given in such a way that the average value of the solution in the considered domain gets a given value. By the method of separation of variables the given problem is reduced to a Volterra integral equation of the first kind. The existence of the control function was proved by the Laplace transform method and an estimate was found for the minimal time at which the given average temperature in the domain is reached.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/50b8d86fdfcf49c18623d0e70c22806a Zobrazit plný text záznamu View record in DOAJ