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 Mathematical notes of NEFU: Year: Volume: Issue: Page: Find

 Mathematical notes of NEFU, 2016, Volume 23, Issue 1, Pages 67–78 (Mi svfu16)

Mathematics

On the first problem for the degenerate parabolic equations with changing time direction

I. M. Petrushko, M. I. Petrushko

Research University MEI, Krasnoznamennaya st., 14, Moscow 111250, Russia

Abstract: We study the properties of solutions of parabolic equations with changing time direction. We prove that the Riesz and Littlewood-Paley conditions for these solutions are equivalent. We demonstrate the unique solvability of the first mixed problem with boundary and initial functions of the space type and also establish the existence of limits in with the weight of the decisions on the sections of the border, which are free from the initial conditions.

Keywords: degenerate equations, changing time direction, functional spaces, integral identities, first mixed problem, solvability.

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UDC: 517.95

Citation: I. M. Petrushko, M. I. Petrushko, “On the first problem for the degenerate parabolic equations with changing time direction”, Mathematical notes of NEFU, 23:1 (2016), 67–78

Citation in format AMSBIB
\Bibitem{PetPet16} \by I.~M.~Petrushko, M.~I.~Petrushko \paper On the first problem for the degenerate parabolic equations with changing time direction \jour Mathematical notes of NEFU \yr 2016 \vol 23 \issue 1 \pages 67--78 \mathnet{http://mi.mathnet.ru/svfu16} \elib{http://elibrary.ru/item.asp?id=27475086}