Geodesic
Blowup of the solution to a nonlinear system of Sobolev-type equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 4, pp. 662-670 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An initial-boundary value problem is considered for a fifth-order nonlinear equation describing the dynamics of a Kelvin–Voigt fluid with allowance for strong spatial dispersion in the presence of sources with a cubic nonlinearity. A local existence theorem is proved. The method of energy inequalities is used to find sufficient conditions for the solution to blowup in a finite time. 
@article{ZVMMF_2009_49_4_a7,
     author = {P. A. Chubenko},
     title = {Blowup of the solution to a~nonlinear system of {Sobolev-type} equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {662--670},
     year = {2009},
     volume = {49},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_4_a7/}
}
TY  - JOUR
AU  - P. A. Chubenko
TI  - Blowup of the solution to a nonlinear system of Sobolev-type equations
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2009
SP  - 662
EP  - 670
VL  - 49
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_4_a7/
LA  - ru
ID  - ZVMMF_2009_49_4_a7
ER  - 
%0 Journal Article
%A P. A. Chubenko
%T Blowup of the solution to a nonlinear system of Sobolev-type equations
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2009
%P 662-670
%V 49
%N 4
%U http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_4_a7/
%G ru
%F ZVMMF_2009_49_4_a7
P. A. Chubenko. Blowup of the solution to a nonlinear system of Sobolev-type equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 4, pp. 662-670. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_4_a7/

[1] Oskolkov A. P., “O razreshimosti v tselom pervoi kraevoi zadachi dlya odnoi kvazilineinoi sistemy tretego poryadka, vstrechayuscheisya pri izuchenii dvizheniya vyazkikh zhidkostei”, Zap. nauchn. seminara LOMI, 27, 1972, 145–160 | MR

[2] Oskolkov A. P., “Nachalno-kraevye zadachi dlya uravnenii zhidkostei Kelvina–Foigta i zhidkostei Oldroita”, Tr. MIAN SSSR, 179, M., 1988, 126–164 | MR

[3] Oskolkov A. P., “Nelokalnye problemy dlya uravnenii zhidkostei Kelvina–Foigta i ikh $\varepsilon$-approksimatsii”, Zap. nauchn. seminara POMI, 221, 1995, 185–207

[4] Oskolkov A. P., “Gladkie skhodyaschiesya $\varepsilon$-approksimatsii pervoi nachalno-kraevoi zadachi dlya uravnenii zhidkostei Kelvina–Foigta”, Zap. nauchn. seminara POMI, 219, 1994, 186–212 | MR

[5] Oskolkov A. P., “O nekotorykh psevdoparabolicheskikh sistemakh uravnenii s malym parametrom, voznikayuschikh pri chislennom analize uravnenii zhidkostei Kelvina–Foigta”, Teoriya uravnenii Soboleva i ee prilozheniya, Gos. un-t, Chelyabinsk, 1994, 113–136 | MR

[6] Gaevskii X., Greger K., Zakharias K., Nelineinye operatornye uravneniya i operatornye differentsialnye uravneniya, Mir, M., 1978 | MR

[7] Sveshnikov A. G., Alshin A. B., Korpusov M. O., Pletner Yu. D., Lineinye i nelineinye uravneniya Sobolevskogo tipa, Nauka, M., 2007

[8] Iosida K., Funktsionalnyi analiz, Mir, M., 1967 | MR

[9] Lions Zh.-L., Nekotorye metody resheniya nelineinykh kraevykh zadach, Mir, M., 1972 | MR

[10] Vainberg M. M., Variatsionnye metody issledovaniya nelineinykh operatorov, Gostekhteorizdat, M., 1956

[11] Demidovich V. P., Lektsii po matematicheskoi teorii ustoichivosti, Nauka, M., 1967 | MR