Geodesic
Extremum problems and control function estimates for a parabolic equation
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2024), pp. 40-50

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider an extremum problem associated with a mathematical model of the temperature control. It is based on a one-dimensional non-self-adjoint parabolic equation of general form. Determining the optimal control as a function minimizing the weighted quadratic functional, we prove the existence of a solution to the problem of the double minimum by control and weight functions. We also obtained upper estimates for the norm of the control function in terms of the value of the functional. These estimates are used to prove the existence of the minimizing function for unbounded sets of control functions. 
@article{VMUMM_2024_1_a4,
     author = {I. V. Astashova and D. A. Lashin and A. V. Filinovskii},
     title = {Extremum problems and control function estimates for a parabolic equation},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {40--50},
     publisher = {mathdoc},
     number = {1},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2024_1_a4/}
}
TY  - JOUR
AU  - I. V. Astashova
AU  - D. A. Lashin
AU  - A. V. Filinovskii
TI  - Extremum problems and control function estimates for a parabolic equation
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2024
SP  - 40
EP  - 50
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2024_1_a4/
LA  - ru
ID  - VMUMM_2024_1_a4
ER  - 
%0 Journal Article
%A I. V. Astashova
%A D. A. Lashin
%A A. V. Filinovskii
%T Extremum problems and control function estimates for a parabolic equation
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2024
%P 40-50
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VMUMM_2024_1_a4/
%G ru
%F VMUMM_2024_1_a4
I. V. Astashova; D. A. Lashin; A. V. Filinovskii. Extremum problems and control function estimates for a parabolic equation. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2024), pp. 40-50. http://geodesic.mathdoc.fr/item/VMUMM_2024_1_a4/