Abstract
In an unbounded noncylindrical domain G we consider classical solutions of general second order linear parabolic equations satisfying a Dirichlet boundary condition on the parabolic part of the boundary of G. On the basis of the maximum principle we single out classes of uniqueness of such solutions depending on the geometry of the domain G which are analogs of the classes of A. N. Tikhonov and S. Täcklind.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 7, pp. 924–930, July, 1990.
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Kurta, V.V., Shishkov, A.E. Uniqueness classes of solutions of boundary problems for nondivergent second order parabolic equations in noncylindrical domains. Ukr Math J 42, 819–825 (1990). https://doi.org/10.1007/BF01062085
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DOI: https://doi.org/10.1007/BF01062085