@article{Dekhkonov2025, 
author = {Farrukh Dekhkonov and Batirkhan Turmetov},
title = {On one time-optimal control problem for a parabolic equation with involution in a bounded domain},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {9},
pages = {20531-20549},
keywords = {parabolic equation, Volterra integral equation, admissible control, minimal time, eigenfunction, involution},
url = {https://www.sciopen.com/article/10.3934/math.2025916},
doi = {10.3934/math.2025916},
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.}
}