The Phase Space of an Initial-Boundary Value Problem for the Hoff Equation
Matematičeskie zametki, Tome 71 (2002) no. 2, pp. 292-297.

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

The Hoff equation $(\lambda +\Delta )u_t=-\alpha u-\beta u^3$ describes the H-beam buckling dynamics. We show that the phase space of the Hoff equation is a simple $C^\infty $ Banach manifold modeled on a subspace complementary to the kernel $\ker (\lambda +\Delta )$.
@article{MZM_2002_71_2_a11,
     author = {G. A. Sviridyuk and V. O. Kazak},
     title = {The {Phase} {Space} of an {Initial-Boundary} {Value} {Problem} for the {Hoff} {Equation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {292--297},
     publisher = {mathdoc},
     volume = {71},
     number = {2},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_71_2_a11/}
}
TY  - JOUR
AU  - G. A. Sviridyuk
AU  - V. O. Kazak
TI  - The Phase Space of an Initial-Boundary Value Problem for the Hoff Equation
JO  - Matematičeskie zametki
PY  - 2002
SP  - 292
EP  - 297
VL  - 71
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2002_71_2_a11/
LA  - ru
ID  - MZM_2002_71_2_a11
ER  - 
%0 Journal Article
%A G. A. Sviridyuk
%A V. O. Kazak
%T The Phase Space of an Initial-Boundary Value Problem for the Hoff Equation
%J Matematičeskie zametki
%D 2002
%P 292-297
%V 71
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2002_71_2_a11/
%G ru
%F MZM_2002_71_2_a11
G. A. Sviridyuk; V. O. Kazak. The Phase Space of an Initial-Boundary Value Problem for the Hoff Equation. Matematičeskie zametki, Tome 71 (2002) no. 2, pp. 292-297. http://geodesic.mathdoc.fr/item/MZM_2002_71_2_a11/

[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), 1516–1526 | MR | Zbl

[3] Sviridyuk G. A., Sukacheva T. G., “Fazovye prostranstva odnogo klassa operatornykh polulineinykh uravnenii tipa Soboleva”, Differents. uravneniya, 26:2 (1990), 250–258 | MR | Zbl

[4] Sviridyuk G. A., “Kvazistatsionarnye traektorii polulineinykh dinamicheskikh uravnenii tipa Soboleva”, Izv. RAN. Ser. matem., 57:3 (1993), 192–207 | Zbl

[5] Sviridyuk G. A., Yakupov M. M., “Fazovoe prostranstvo nachalno-kraevoi zadachi dlya sistemy Oskolkova”, Differents. uravneniya, 32:11 (1996), 1538–1543 | MR | Zbl

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

[7] Leng S., Vvedenie v teoriyu differentsiruemykh mnogoobrazii, Platon, Volgograd, 1996

[8] Sviridyuk G. A., Sukacheva T. G., Dudko L. L., “Otnositelnaya $\sigma$-ogranichennost lineinykh operatorov”, Izv. vuzov. Matem., 1997, no. 7, 68–73 | MR | Zbl

[9] Bokareva T. A., Sviridyuk G. A., “Sborki Uitni fazovykh prostranstv nekotorykh polulineinykh uravnenii tipa Soboleva”, Matem. zametki, 55:3 (1994), 3–10 | MR | Zbl