Abstract
In the strip Q{0<t ≤T, 0<x <∞ } we consider a linear second-order parabolic equation which is degenerate on the boundary t=0, x=0. Assuming that the coefficient of the time derivative has a zero of a sufficiently high order at 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.
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Translated from Matematicheskie Zametki, Vol. 12, No. 5, pp. 643–652, November, 1972
The author wishes to thank S. N. Kruzhkov and O. A. Oleinik for a number of useful discussions.
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Dzhuraev, T.D. Boundary value problems for linear parabolic equations degenerate on the boundary of a region. Mathematical Notes of the Academy of Sciences of the USSR 12, 822–827 (1972). https://doi.org/10.1007/BF01099074
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DOI: https://doi.org/10.1007/BF01099074