We consider the Cauchy problem in the half-space for a parabolic equation with unbounded initial data and lower order coefficients. We establish the solvability of the problem in the weighted space of Hölder functions such that the functions, together with their derivatives, admit exponential growth as t → ∞ and, near the plane t = 0, the derivatives grow not faster than a power function. Bibliography: 11 titles.
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Translated from Problemy Matematicheskogo Analiza 82, September 2015, pp. 165-183.
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Cherepova, M.F. Solvability of the Cauchy Problem for a Parabolic Equation with Unbounded Coefficients. J Math Sci 210, 736–757 (2015). https://doi.org/10.1007/s10958-015-2587-y
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DOI: https://doi.org/10.1007/s10958-015-2587-y