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

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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},
     publisher = {mathdoc},
     volume = {49},
     number = {4},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_4_a7/}
}
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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/