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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2009, Volume 49, Number 4, Pages 662–670 (Mi zvmmf8)  
Blowup of the solution to a nonlinear system of Sobolev-type equations

P. A. Chubenko

Faculty of Physics, Moscow State University, Moscow, 119992, Russia
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Abstract: 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.
Key words: Kelvin–Voigt fluid, Sobolev-type equation, strong generalized solution, contraction mapping principle, method of differential inequalities, solution blowup.
Received: 16.05.2008
English version:
Computational Mathematics and Mathematical Physics, 2009, Volume 49, Issue 4, Pages 638–646
DOI: https://doi.org/10.1134/S0965542509040083
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
Citation: P. A. Chubenko, “Blowup of the solution to a nonlinear system of Sobolev-type equations”, Zh. Vychisl. Mat. Mat. Fiz., 49:4 (2009), 662–670; Comput. Math. Math. Phys., 49:4 (2009), 638–646
Citation in format AMSBIB
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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