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Tr. Mosk. Mat. Obs., 2014, Volume 75, Issue 2, Pages 277–308 (Mi mmo567)  

This article is cited in 2 scientific papers (total in 2 papers)

Necessary and sufficient condition for the stabilization of the solution of a mixed problem for nondivergence parabolic equations to zero

Yu. A. Alkhutova, V. N. Denisovb

a Vladimir State University
b M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: We consider the first boundary value problem in a cylindrical domain for a uniformly parabolic second-order equation in nondivergence form. The solution satisfies the homogeneous Dirichlet condition on the lateral surface of the cylinder, and the initial function is bounded. We show that if the coefficients of the equation satisfy the local and global Dini conditions, then a necessary and sufficient condition for the stabilization of the solution to zero coincides with a similar condition for the heat equation.

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English version:
Transactions of the Moscow Mathematical Society, 2014, 75, 233–258

UDC: 517.956
MSC: 35K10
Received: 29.03.2014

Citation: Yu. A. Alkhutov, V. N. Denisov, “Necessary and sufficient condition for the stabilization of the solution of a mixed problem for nondivergence parabolic equations to zero”, Tr. Mosk. Mat. Obs., 75, no. 2, MCCME, M., 2014, 277–308; Trans. Moscow Math. Soc., 75 (2014), 233–258

Citation in format AMSBIB
\Bibitem{AlkDen14}
\by Yu.~A.~Alkhutov, V.~N.~Denisov
\paper Necessary and sufficient condition for the stabilization of the solution of~a~mixed problem for nondivergence parabolic equations to zero
\serial Tr. Mosk. Mat. Obs.
\yr 2014
\vol 75
\issue 2
\pages 277--308
\publ MCCME
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo567}
\elib{https://elibrary.ru/item.asp?id=23780166}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2014
\vol 75
\pages 233--258
\crossref{https://doi.org/10.1090/S0077-1554-2014-00233-8}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84960098271}


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    This publication is cited in the following articles:
    1. E. Lanconelli, G. Tralli, F. Uguzzoni, “Wiener-type tests from a two-sided Gaussian bound”, Ann. Mat. Pura Appl., 196:1 (2017), 217–244  crossref  mathscinet  zmath  isi  scopus
    2. A. A. Kon'kov, “Geometric estimates of solutions of quasilinear elliptic inequalities”, Izv. Math., 84:6 (2020), 1056–1104  mathnet  crossref  crossref
  • Trudy Moskovskogo Matematicheskogo Obshchestva
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