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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1972, Volume 12, Issue 5, Pages 643–652 (Mi mz9928)

Boundary value problems for linear parabolic equations degenerate on the boundary of a region

T. D. Dzhuraev

Institute of Mathematics, Academy of Sciences of the Uzbek SSR

Abstract: In the strip $\mathrm{Q\{ 0<t\leqslant T, 0<x<\infty \}}$ we consider a linear second-order parabolic equation which is degenerate on the boundary $\mathrm{t=0}$, $\mathrm{x=0}$. Assuming that the coefficient of the time derivative has a zero of a sufficiently high order at $\mathrm{t=0}$, we find the sufficient conditions to ensure the correctness of certain boundary value problems. One of these problems occurs in the theory of the temperature boundary layer.

Full text: PDF file (1097 kB)

English version:
Mathematical Notes, 1972, 12:5, 822–827

Bibliographic databases:

UDC: 517.9

Citation: T. D. Dzhuraev, “Boundary value problems for linear parabolic equations degenerate on the boundary of a region”, Mat. Zametki, 12:5 (1972), 643–652; Math. Notes, 12:5 (1972), 822–827

Citation in format AMSBIB
\Bibitem{Dzh72} \by T.~D.~Dzhuraev \paper Boundary value problems for linear parabolic equations degenerate on the boundary of a region \jour Mat. Zametki \yr 1972 \vol 12 \issue 5 \pages 643--652 \mathnet{http://mi.mathnet.ru/mz9928} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=322348} \zmath{https://zbmath.org/?q=an:0244.35053} \transl \jour Math. Notes \yr 1972 \vol 12 \issue 5 \pages 822--827 \crossref{https://doi.org/10.1007/BF01099074}