Geodesic
Investigation of the solvability of the first boundary -- value problem for the parabolic equation under the nonfulfillment of the compatibility conditions of the initial and boundary data
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 49, Tome 508 (2021), pp. 39-72

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There is studied the first boundary – value problem for the parabolic equation of second order under the nonfulfillment of the compatibility conditions of the initial and boundary data. Existence, uniqueness, estimates of the solution are established. It is proved that the solution of the problem is the sum of the Hölder and singular functions that belong to the weighted Hölder spaces. 
@article{ZNSL_2021_508_a1,
     author = {G. I. Bizhanova},
     title = {Investigation of the solvability of the first boundary -- value problem for the parabolic equation under the nonfulfillment of the compatibility conditions of the initial and boundary data},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {39--72},
     publisher = {mathdoc},
     volume = {508},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_508_a1/}
}
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G. I. Bizhanova. Investigation of the solvability of the first boundary -- value problem for the parabolic equation under the nonfulfillment of the compatibility conditions of the initial and boundary data. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 49, Tome 508 (2021), pp. 39-72. http://geodesic.mathdoc.fr/item/ZNSL_2021_508_a1/