Geodesic
Averaged controllability of thermoelasticity equations. Average state of a rectangular plate
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 55 (2021) no. 2, pp. 123-130.

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

The concept of averaged controllability has been introduced relatively recently aiming to analyse the controllability of systems or processes containing some important parameters that may affect the controllability in usual sense. The averaged controllability of various specific and abstract equations has been studied so far. Relatively little attention has been paid to averaged controllability of coupled systems. The averaged state of a thermoelastic rectangular plate is studied in this paper using the well-known Green's function approach. The aim of the paper is to provide a theoretical background for further exact and approximate controllability analysis of fully coupled thermoelasticity equations, which will appear elsewhere
Keywords: averaged controllability, mathematical expectation, controllability of PDEs. 
@article{UZERU_2021_55_2_a2,
     author = {S. H. Jilavyan and A. Zh. Khurshudyan},
     title = {Averaged controllability of thermoelasticity equations. {Average} state of a rectangular plate},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {123--130},
     publisher = {mathdoc},
     volume = {55},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UZERU_2021_55_2_a2/}
}
TY  - JOUR
AU  - S. H. Jilavyan
AU  - A. Zh. Khurshudyan
TI  - Averaged controllability of thermoelasticity equations. Average state of a rectangular plate
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 2021
SP  - 123
EP  - 130
VL  - 55
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UZERU_2021_55_2_a2/
LA  - en
ID  - UZERU_2021_55_2_a2
ER  - 
%0 Journal Article
%A S. H. Jilavyan
%A A. Zh. Khurshudyan
%T Averaged controllability of thermoelasticity equations. Average state of a rectangular plate
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 2021
%P 123-130
%V 55
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UZERU_2021_55_2_a2/
%G en
%F UZERU_2021_55_2_a2
S. H. Jilavyan; A. Zh. Khurshudyan. Averaged controllability of thermoelasticity equations. Average state of a rectangular plate. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 55 (2021) no. 2, pp. 123-130. http://geodesic.mathdoc.fr/item/UZERU_2021_55_2_a2/

[1] A. S. Avetisyan, A. Zh. Khurshudyan, Controllability of Dynamic Systems: The Green's Function Approach., Cambridge Scholars Publishing, Cambridge, 2018

[2] E. Zuazua, “Averaged Control.”, Automatica, 50:12 (2014), 3077–3087 | DOI | MR | Zbl

[3] Q. Lü, E. Zuazua, “Averaged Controllability for Random Evolution Partial Differential Equations”, Journal de Mathématiques Pures et Appliquées, 105:3 (2016), 367–414 | DOI | MR | Zbl

[4] M. Lazar, E. Zuazua, “Averaged Control and Observation of Parameter Depending Wave Equations”, Math. Acad. Sci. Paris, 352:6 (2014), 497–502 | DOI | MR | Zbl

[5] J. Lohéac, E. Zuazua, “Averaged Controllability of Parameter Dependent Conservative Semigroups”, J. Diff. Equat., 262:3 (2017), 1540–1574 | DOI | MR | Zbl

[6] Q. Lü, E. Zuazua, Averaged Controllability for Parameter Dependent Evolution Partial Differential Equations. Open Problems in Systems and Control, IMA-Minneapolis, 2017, 4 pp.

[7] J. Klamka, As. Zh. Khurshudyan, “Averaged Controllability of Heat Equation in Unbounded Domains with Uncertain Geometry and Location of Controls: The Green's Function Approach”, Archives of Control Sciences, 29(65):4 (2019), 573–584 | DOI | MR | Zbl

[8] A. S. Avetisyan, As. Zh Khurshudyan, “Averaged Controllability of Euler Bernoulli Beam Structures with Random Parameters: The Green's Function Approach”, Proceedings of NAS of Armenia. Mechanics, 72:4 (2019), 6–16 | DOI

[9] W. Nowacki, Thermoelasticity, Pergamon Press, N. Y., 1986, 578 pp. | MR | Zbl

[10] A. D. Polyanin, V. E. Nazaikinskii, Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd ed., CRC Press, Boca Raton, 2016 | MR | Zbl