Geodesic
Invariant manifolds of the Hoff equation
Matematičeskie zametki, Tome 79 (2006) no. 3, pp. 444-449.

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The Hoff equation $(\lambda+\Delta)u_t=-\alpha u-\beta u^3$ models the buckling of a T-shaped beam, where $\lambda$, $\alpha$, and $\beta\in\mathbb R_+$ are the parameters of the model. The existence of a finite-dimensional local invariant manifold is established in the neighborhood of zero. 
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G. A. Sviridyuk; O. G. Kitaeva. Invariant manifolds of the Hoff equation. Matematičeskie zametki, Tome 79 (2006) no. 3, pp. 444-449. http://geodesic.mathdoc.fr/item/MZM_2006_79_3_a10/

[1] Volmir A. S., Ustoichivost deformiruemykh sistem, Nauka, M., 1967

[2] Sidorov N. A., Romanova O. A., “O primenenii nekotorykh rezultatov teorii vetvleniya pri reshenii differentsialnykh uravnenii”, Differents. uravneniya, 19:9 (1983), 1526–1526 | Zbl

[3] Sviridyuk G. A., “Kvazistatsionarnye traektorii polulineinykh dinamicheskikh uravnenii tipa Soboleva”, Izv. RAN. Ser. matem., 57:3 (1993), 192–202

[4] Sviridyuk G. A., Kazak V. O., “Fazovoe prostranstvo nachalno-kraevoi zadachi dlya uravneniya Khoffa”, Matem. zametki, 71:2 (2002), 292–297 | Zbl

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

[6] Sviridyuk G. A., Sukacheva E. G., “Zadacha Koshi dlya odnogo klassa polulineinykh uravnenii tipa Soboleva”, Sib. matem. zh., 31:5 (1990), 109–119 | MR | Zbl

[7] Sviridyuk G. A., “K obschei teorii polugrupp operatorov”, UMN, 49:4 (1994), 47–74 | Zbl

[8] Lent S., Vvedenie v teoriyu differentsiruemykh mnogoobrazii, Platon, Volgograd, 1996

[9] Sviridyuk G. A., Keller A. V., “Invariantnye prostranstva i dikhotomii reshenii odnogo klassa lineinykh uravnenii tipa Soboleva”, Izv. vuzov. Matem., 1997, no. 5, 60–68 | Zbl