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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

[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