Geodesic
On the blow-up of internal gravitational waves with non-linear sources
Izvestiya. Mathematics , Tome 75 (2011) no. 4, pp. 691-710.

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We consider an equation of internal gravitational waves in a stratified fluid in which non-linear sources of a general form are taken into account. In the case of the corresponding initial-boundary-value problem in a bounded domain with homogeneous Dirichlet conditions on the boundary, we prove the local-in-time solubility and also obtain sufficient conditions for the blow-up of a solution in finite time.
Keywords: blow-up, non-linear initial-boundary-value problem, internal waves, equation of Sobolev type. 
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M. O. Korpusov. On the blow-up of internal gravitational waves with non-linear sources. Izvestiya. Mathematics , Tome 75 (2011) no. 4, pp. 691-710. http://geodesic.mathdoc.fr/item/IM2_2011_75_4_a2/

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