Geodesic
The stability of the Hoff linear equations on a graph
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, no. 5 (2010), pp. 11-16
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The stability of stationary solution of the Hoff linear equations on a graph which is a model design of I-beams is considered. The main approach is the second Lyapunov method modifying respectively to our situation.
Mots-clés : Sobolev type equation
Keywords: graph, phase spase, Lyapunov function. 
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S. A. Zagrebina; P. O. Pivovarova. The stability of the Hoff linear equations on a graph. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, no. 5 (2010), pp. 11-16. http://geodesic.mathdoc.fr/item/VYURU_2010_5_a1/

[1] G. A. Sviridyuk, V. V. Shemetova, “Uravneniya Khoffa na grafakh”, Differents. uravneniya, 42:1 (2006), 126–131

[2] Pokornyi Yu. V., Penkin O. M., Pryadiev V. L. i dr., Differentsialnye uravneniya na geometricheskikh grafakh, Fizmatlit, M., 2004 | Zbl

[3] G. V. Demidenko, S. V. Uspenskii, Partial differential equations and systems not solvable with respect to the highest-order derivative, Marcel Dekker, Inc., N. Y.–Basel–Hong Kong, 2003 | MR | Zbl

[4] Sveshnikov A. G., Alshin A. B., Korpusov M. O., Pletner Yu. D., Lineinye i nelineinye uravneniya sobolevskogo tipa, Fizmatlit, M., 2007

[5] G. A. Sviridyuk, “Uravneniya sobolevskogo tipa na grafakh”, Neklassicheskie uravneniya matematicheskoi fiziki, Sb. nauch. rabot, Novosibirsk, 2002, 221–225

[6] G. A. Sviridyuk, V. E. Fedorov, Linear Sobolev Type Equations and Degenerate Semigroups of Operators, VSP, Utrecht–Boston, 2003 | MR | Zbl

[7] A. A. Zamyshlyaeva, “Fazovye prostranstva odnogo klassa lineinykh uravnenii sobolevskogo tipa vtorogo poryadka”, Vychislit. tekhnologii, 8:4 (2003), 45–54 | MR

[8] N. A. Manakova, “Zadacha optimalnogo upravleniya dlya uravneniya Oskolkova nelineinoi filtratsii”, Differents. uravneniya, 43:9 (2007), 1185–1192 | MR | Zbl

[9] A. V. Keller, “Chislennoe reshenie zadachi startovogo upravleniya dlya sistemy uravnenii leontevskogo tipa”, Obozrenie priklad. i prom. matematiki, 16:2 (2009), 345–346

[10] G. A. Sviridyuk, A. V. Keller, “Invariantnye prostranstva i dikhotomii reshenii odnogo klassa lineinykh uravnenii tipa Soboleva”, Izv. VUZ. Matematika, 1997, no. 5, 60–68 | MR

[11] O. G. Kitaeva, G. A. Sviridyuk, “Ustoichivoe i neustoichivoe invariantnye mnogoobraziya uravneniya Oskolkova”, Neklassicheskie uravneniya matematicheskoi fiziki, Novosibirsk, 2005, 160–166 | MR

[12] S. A. Zagrebina, “O suschestvovanii i ustoichivosti reshenii uravnenii Nave–Stoksa”, Vestn. MaGU. Ser. Matematika, 2005, no. 8, 74–86

[13] S. A. Zagrebina, M. M. Yakupov, “Suschestvovanie i ustoichivost reshenii odnogo klassa polulineinykh uravnenii sobolevskogo tipa”, Vestn. YuUrGU. Ser. «Matematicheskoe modelirovanie i programmirovanie», 27(127):2 (2008), 10–18 | Zbl

[14] D. Khenri, Geometricheskaya teoriya polulineinykh parabolicheskikh uravnenii, Mir, M., 1985 | MR