Geodesic
Parabolic equations with changing direction of time
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 491 (2020), pp. 82-85

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A theorem about the behavior of Cauchy-type integrals at the endpoints of the integration contour and at discontinuity points of the density is stated, and its application to boundary value problems for $2n$-order parabolic equations with a changing direction of time are described. The theory of singular equations, along with the smoothness of the initial data, makes it possible to specify necessary and sufficient conditions for the solution to belong to Hölder spaces. Note that, in the case $n=3$, the smoothness of the initial data and the solvability conditions imply that the solution belongs to smoother spaces near the ends with respect to the time variable.
Keywords: Cauchy-type integral, parabolic equations with changing direction of time, bonding gluing condition, Hölder space, singular integral equation. 
@article{DANMA_2020_491_a16,
     author = {S. V. Popov},
     title = {Parabolic equations with changing direction of time},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {82--85},
     publisher = {mathdoc},
     volume = {491},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_491_a16/}
}
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S. V. Popov. Parabolic equations with changing direction of time. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 491 (2020), pp. 82-85. http://geodesic.mathdoc.fr/item/DANMA_2020_491_a16/