Browsing by Subject "parabolic equation"

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Access status: Open Access ,
On properties of minimizers of a control problem with time-distributed functional related to parabolic equations
(Wydawnictwa AGH, 2019) Astašova, Irina Viktorovna; Filinovskij, Aleksej Vladislavovič
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.
Access status: Open Access ,
On the Tonelli method for the degenerate parabolic Cauchy problem with functional argument
(2014) Topolski, Krzysztof A.
The degenerate parabolic Cauchy problem is considered. A functional argument in the equation is of the Hale type. As a limit of piecewise classical solutions we obtain a viscosity solution of the main problem. Presented method is an adaptation of Tonelli's constructive method to the partial differential-functional equation. It is also shown that this approach can be improved by the vanishing viscosity method and regularization process.