Work

On one time-optimal control problem for a parabolic equation with involution in a bounded domain

Year: 2025

Type: article

Abstract: In this paper, we study the problem of time-optimal control for the parabolic equation with involution in a multidimensional parallelepiped domain. A generalized solution to the initial boundary value problem is found, and the control problem is reduced to a first-order Volterra integral equation. To prove the existence and uniqueness of the solution to this integral equation, necessary estimates are obtained for its kernel. The existence of a solution to the integral equation, i.e., the admissibility of the control function, is proven, and an optimal estimate of the minimum time required to heat the domain to a certain average temperature is found.

Source: AIMS Mathematics

DOI: 10.3934/math.2025916

Authors: Farrukh Dekhkonov, Batirkhan Turmetov

Institutions: Namangan State University, Ahmet Yesevi University, Alfraganus University

Language: English

Topic: Differential Equations and Boundary Problems

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

OpenAlex ID: W4414220600