We study a conjugation problem for the second-order parabolic equation with a parabolic operator of the same order in the conjugation condition and with a boundary condition of the first boundary-value problem set on the exterior part of the domain boundary. Using a method of potential theory, we prove the classical solvability of the problem in the Hölder function space.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 7–16, January–March, 2008.
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Kopytko, B.I., Tsapovs’ka, Z.Y. Initial boundary-value problem with Wentzel-type conjugation condition for a parabolic equation with discontinuous coefficients. J Math Sci 160, 283–295 (2009). https://doi.org/10.1007/s10958-009-9497-9
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DOI: https://doi.org/10.1007/s10958-009-9497-9