The Cauchy problem for the second order parabolic equation with singular coefficients with respect to t at the first order spatial derivatives, is considered. A solution to this problem is constructed in explicit form. To this purpose a weighted Hölder space with positive power of t as the weight, is defined. The existence, uniqueness, and estimates of the solution are proved.
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Dedicated to the 85th jubilee of V. A. Solonnikov
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 477, 2018, pp. 35–53.
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Bizhanova, G.I. A Solution to the Cauchy Problem for Parabolic Equation with Singular Coefficients. J Math Sci 244, 946–958 (2020) doi:10.1007/s10958-020-04666-8