Geodesic
On the blow-up of a~solution of a~non-local system of equations of hydrodynamic type
Izvestiya. Mathematics , Tome 76 (2012) no. 1, pp. 190-213

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We study Oskolkov's non-linear non-local system of equations with a source and the applicability of an operator method. We prove the existence of a weak solution of the initial-boundary value problem for this system and investigate uniqueness conditions for a weak solution. Sufficient conditions for the blow-up of a solution of the problem are found and upper and lower bounds are obtained for the time of blowing up of a solution. We also consider the smoothness problem for a weak solution.
Keywords: blow-up of a solution, system of hydrodynamic type, non-local initial-boundary value problem. 
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     author = {E. V. Yushkov},
     title = {On the blow-up of a~solution of a~non-local system of equations of hydrodynamic type},
     journal = {Izvestiya. Mathematics },
     pages = {190--213},
     publisher = {mathdoc},
     volume = {76},
     number = {1},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2012_76_1_a7/}
}
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E. V. Yushkov. On the blow-up of a~solution of a~non-local system of equations of hydrodynamic type. Izvestiya. Mathematics , Tome 76 (2012) no. 1, pp. 190-213. http://geodesic.mathdoc.fr/item/IM2_2012_76_1_a7/