On one time-optimal control problem for a parabolic equation with involution in a bounded domain
Dekhkonov F. Turmetov B.
2025American Institute of Mathematical Sciences
AIMS Mathematics
2025#10Issue 920531 - 20549 pp.
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.
admissible control , eigenfunction , involution , minimal time , parabolic equation , Volterra integral equation
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Department of Mathematics, Namangan State University, Namangan, Uzbekistan
Department of Mathematics, Khoja Akhmet Yassawi International Kazakh-Turkish University, Turkistan, Kazakhstan
Department of Mathematics, Alfraganus University, Tashkent, Uzbekistan
Department of Mathematics
Department of Mathematics
Department of Mathematics
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