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

Astashova I. V., Filinovskiy A. V.

Opuscula Mathematica

2019

Vol. 39, no. 5

595--609

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.

On extremals of a variational problem arising in crystallography

Zaslavski A. J.

Journal of Mathematics and Applications

2007

Vol. 29

157-166

In this paper we study the structure of minirnizers of variational problems which were introduced by Hannon, Marcus and Mizel (ESAIM Control Optim. Calc. Var., 2003) to describe step-terraces on surfaces of so-called "unorthodox" crystals. These variational problems are associated with two positive parameters. We will show that if one of these parameters is not smali and the second parameter is large, then the rainimizer is a constant function.