Geodesic
Modelling unsteady processes in semiconductors using a~non-linear Sobolev equation
Izvestiya. Mathematics , Tome 78 (2014) no. 3, pp. 427-442.

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We study an initial-boundary value problem for a non-linear Sobolev equation containing a summand non-local in time and an inhomogeneity. The equation simulates unsteady processes in semiconductors. We find sufficient conditions for the unique solubility of the problem, both global in time and local (rather than global). In the case when the problem is soluble only locally, we find upper and lower bounds for the lifespan of a solution.
Keywords: equations of Sobolev type, blow-up of solutions, method of energy estimates. 
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A. I. Aristov. Modelling unsteady processes in semiconductors using a~non-linear Sobolev equation. Izvestiya. Mathematics , Tome 78 (2014) no. 3, pp. 427-442. http://geodesic.mathdoc.fr/item/IM2_2014_78_3_a0/

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