Geodesic
On stability control of a parabolic systems with distributed parameters on the graph
Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 123, pp. 368-376

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

The work is an attempt to demonstrate the concept of sustainability in the undisturbed state Lyapunov differential system for equations with partial derivatives, and show the ability to use a famous classical results in the studied case.
Keywords: system of parabolic equations, distributed parameters on the graph, initial-boundary value problem, equivalent of Lyapunov stability. 
A. P. Zhabko; V. V. Provotorov; E. N. Provotorova. On stability control of a parabolic systems with distributed parameters on the graph. Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 123, pp. 368-376. http://geodesic.mathdoc.fr/item/VTAMU_2018_23_123_a3/
@article{VTAMU_2018_23_123_a3,
     author = {A. P. Zhabko and V. V. Provotorov and E. N. Provotorova},
     title = {On stability control of a parabolic systems with distributed parameters on the graph},
     journal = {Vestnik rossijskih universitetov. Matematika},
     pages = {368--376},
     year = {2018},
     volume = {23},
     number = {123},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2018_23_123_a3/}
}
TY  - JOUR
AU  - A. P. Zhabko
AU  - V. V. Provotorov
AU  - E. N. Provotorova
TI  - On stability control of a parabolic systems with distributed parameters on the graph
JO  - Vestnik rossijskih universitetov. Matematika
PY  - 2018
SP  - 368
EP  - 376
VL  - 23
IS  - 123
UR  - http://geodesic.mathdoc.fr/item/VTAMU_2018_23_123_a3/
LA  - ru
ID  - VTAMU_2018_23_123_a3
ER  - 
%0 Journal Article
%A A. P. Zhabko
%A V. V. Provotorov
%A E. N. Provotorova
%T On stability control of a parabolic systems with distributed parameters on the graph
%J Vestnik rossijskih universitetov. Matematika
%D 2018
%P 368-376
%V 23
%N 123
%U http://geodesic.mathdoc.fr/item/VTAMU_2018_23_123_a3/
%G ru
%F VTAMU_2018_23_123_a3

[1] V. V. Provotorov, E. N. Provotorova, “Synthesis of optimal boundary control of parabolic system with time-delay and distributed parameters on the graph”, Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 13:2 (2017), 89–104 (In Russian) | MR

[2] V. V. Provotorov, A. S. Volkova, Initial-Boundary Value Problems with Distributed Parameters on the Graph, The Scientific Book Publishing House, Voronezh, 2014, 188 pp. (In Russian)

[3] A. S. Volkova, V. V. Provotorov, “Generalized solutions and generalized eigenfunctions of boundary-value problems on a geometric graph”, Russian Mathematics, 2014, no. 3, 3–18 (In Russian)

[4] J.-L. Lions, Some Methods for Solving Nonlinear Boundary Problems, Mir Publ., Moscow, 1972, 581 pp. (In Russian)

[5] A. P. Zhabko, E. D. Kotina, O. N. Chizhova, Differential Equation and Stability, Lan' Publ., St. Petersburg, 2015, 320 pp. (In Russian)

[6] S. L. Podvalnyy, V. V. Provotorov, “Determining the starting function in the problem of observation of parabolic system with distributed parameters on the graph”, Proceedings of Voronezh State Technical University, 10:6 (2014), 29–35 (In Russian)

[7] V. V. Provotorov, V. I. Ryazhskikh, Yu. A. Gnilitskaya, “Unique weak solvability of a nonlinear initial boundary value problem with distributed parameters in a netlike region”, Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 13:3 (2017), 264–277 (In Russian) | MR