Opuscula Math. 39, no. 5 (2019), 595-609

Opuscula Mathematica

On properties of minimizers of a control problem with time-distributed functional related to parabolic equations

I. V. Astashova
A. V. Filinovskiy

Abstract. We consider a control problem given by a mathematical model of the temperature control in industrial hothouses. The model is based on one-dimensional parabolic equations with variable coefficients. The optimal control is defined as a minimizer of a quadratic cost functional. We describe qualitative properties of this minimizer, study the structure of the set of accessible temperature functions, and prove the dense controllability for some set of control functions.

Keywords: parabolic equation, extremal problem, quadratic cost functional, minimizer, exact controllability, dense controllability.

Mathematics Subject Classification: 35K20, 35Q93, 35Q79, 49J20.

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  • Communicated by P.A. Cojuhari.
  • Received: 2019-02-01.
  • Revised: 2019-06-06.
  • Accepted: 2019-06-18.
  • Published online: 2019-09-05.
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Cite this article as:
I. V. Astashova, A. V. Filinovskiy, On properties of minimizers of a control problem with time-distributed functional related to parabolic equations, Opuscula Math. 39, no. 5 (2019), 595-609, https://doi.org/10.7494/OpMath.2019.39.5.595

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