Popov, S. V. Parabolic equations with changing direction of time. (English. Russian original) Zbl 1477.35307 Dokl. Math. 101, No. 2, 147-149 (2020); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 491, 82-85 (2020). Summary: 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. Cited in 1 Document MSC: 35R25 Ill-posed problems for PDEs 35K35 Initial-boundary value problems for higher-order parabolic equations Keywords:Cauchy-type integral; parabolic equations with changing direction of time; bonding gluing condition; Hölder space; singular integral equation × Cite Format Result Cite Review PDF Full Text: DOI References: [1] F. D. Gakhov, Boundary Value Problems (Nauka, Moscow, 1977; Dover, New York, 1990). · Zbl 0449.30030 [2] N. I. Muskhelishvili, Singular Integral Equations (Nauka, Moscow, 1968; Wolters-Noordhoff, Groningen, 1972). · Zbl 0174.16202 [3] Tersenov, S. A., Parabolic Equations with Changing Direction of Time (1985), Novosibirsk: Nauka, Novosibirsk · Zbl 0582.35001 [4] V. N. Monakhov, Boundary Value Problems with Free Boundaries for Elliptic Systems of Equations (Nauka, Novosibirsk, 1977; Am. Math. Soc., Providence, R.I., 1983). · Zbl 0532.35002 [5] N. P. Vekua, Systems of Singular Integral Equations (Noordhoff, Groningen, 1967; Nauka, Moscow, 1968). · Zbl 0166.09802 [6] Doduchava, R. V., Dokl. Akad. Nauk SSSR, 191, 16-19 (1970) [7] Soldatov, A. P., One-Dimensional Singular Operators and Boundary Value Problems in Function Theory (1991), Moscow: Vysshaya Shkola, Moscow · Zbl 0774.47025 [8] Popov, S. V., Dokl. Math., 71, 23-25 (2005) [9] S. V. Popov, “Solvability of boundary value problems for a high-order parabolic equation with changing direction of time,” Available from VINITI, No. 8646-B88 (Novosibirsk, 1988). [10] Popov, S. V.; Potapova, S. V., Dokl. Math., 79, 100-102 (2009) · Zbl 1269.35011 · doi:10.1134/S106456240901030X [11] Popov, S. V., Mat. Zametki Sev. Vost. Fed. Univ., 21, 81-93 (2014) · Zbl 1340.35104 [12] Cattabriga, L., Rend. Sem. Mat. Univ. Padova, 28, 376-401 (1958) · Zbl 0102.09101 [13] Cattabriga, L., Rend. Sem. Fac. Sc. Univ. Cagliari, 31, 48-79 (1961) · Zbl 0252.35037 [14] Rend. Sem. Fac. Sc. Univ. Cagliari 32 (3-4), 254-267 (1962). · Zbl 0252.35038 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.