Geodesic
Solution of the Cauchy problem for a parabolic equation with singular coefficients
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 47, Tome 477 (2018), pp. 35-53

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The paper is concerned with the Cauchy problem for the second order parabolic equation with the singular coefficients with respect to $t$ at the first order spatial derivatives. The solution of the problem is constructed in the explicit form. For it, it is defined a weighted Hölder space with the weight as a positive power of $t$. The existence, uniqueness, estimates of the solution are proved. 
@article{ZNSL_2018_477_a2,
     author = {G. I. Bizhanova},
     title = {Solution of the {Cauchy} problem for a parabolic equation with singular coefficients},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {35--53},
     publisher = {mathdoc},
     volume = {477},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_477_a2/}
}
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G. I. Bizhanova. Solution of the Cauchy problem for a parabolic equation with singular coefficients. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 47, Tome 477 (2018), pp. 35-53. http://geodesic.mathdoc.fr/item/ZNSL_2018_477_a2/