On the time-optimal control problem associated with the epitaxial growth of thin film

In this paper, we consider the optimal time control problem for a fourth-order parabolic equation describing the growth process of a thin film in a bounded domain. The control function is defined on a certain part of a boundary. An optimal estimate of the minimum time required for a thin film to reach a given average height is found.

Authors

Publication Details

Journal
Uzbek Mathematical Journal
Published
2025-02-13
DOI
https://doi.org/10.29229/uzmj.2024-4-4
Primary Topic
Fluid Dynamics and Thin Films
Type
article
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article

On the time-optimal control problem associated with the epitaxial growth of thin film

F.N. Dekhkonov
2 links
Uzbek Mathematical Journal
Fluid Dynamics and Thin Films
article

On the time-optimal control problem associated with the epitaxial growth of thin film

F.N. Dekhkonov
article en

Abstract

In this paper, we consider the optimal time control problem for a fourth-order parabolic equation describing the growth process of a thin film in a bounded domain. The control function is defined on a certain part of a boundary. An optimal estimate of the minimum time required for a thin film to reach a given average height is found.

Uzbek Mathematical JournalVol. 68(4)
Openalex Percentile: Top 97%
Fluid Dynamics and Thin Films
DOISourceOpenAlex
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On the time-optimal control problem associated with the epitaxial growth of thin film — F.N. Dekhkonov · Uzbek Mathematical Journal (2025) | TGRS Research Map | TGRS