On the time-optimal control problem for a fourth order parabolic equation in the three-dimensional space

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Abstract

In this paper, we consider the problem of optimal time control for a fourth-order parabolic-type equation describing the growth process of a thin film in a bounded three-dimensional space. The control function is defined on a certain part of a boundary. It is proved that the optimal time depends on the parameters of the growth process when the average value of the growth interface height of the thin film in the domain is close to the critical value.

Keywords

fourth order parabolic equation / Volterra integral equation / admissible control / initial-boundary problem / critical value / minimal time

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