Geodesic
Contact problem for a second-order parabolic equation with Dini-continuous coefficients
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings – XXXI". Voronezh, May 3-9, 2020, Tome 204 (2022), pp. 135-145.

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We consider a contact problem for second-order parabolic equations with Dini-continuous coefficients in a strip divided by a nonsmooth curve into two domains. The existence and uniqueness of a regular solution to this problem is proved.
Keywords: parabolic contact problem, parabolic equation with discontinuous coefficients, method of boundary integral equations, simple layer potential. 
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S. I. Saharov. Contact problem for a second-order parabolic equation with Dini-continuous coefficients. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings – XXXI". Voronezh, May 3-9, 2020, Tome 204 (2022), pp. 135-145. http://geodesic.mathdoc.fr/item/INTO_2022_204_a13/

[1] Baderko E. A., “Kraevye zadachi dlya parabolicheskogo uravneniya i granichnye integralnye uravneniya”, Differ. uravn., 28:1 (1992), 17–23 | MR

[2] Baderko E. A., “Metod teorii potentsiala v kraevykh zadachakh dlya $2m$-parabolicheskikh uravnenii v poluogranichennoi oblasti s negladkoi bokovoi granitsei”, Differ. uravn., 24:1 (1988), 3–9 | MR | Zbl

[3] Baderko E. A., “O parabolicheskoi kraevoi zadache v oblasti prostogo vida”, Differ. uravn., 27:1 (1991), 17–29 | MR

[4] Baderko E. A., “O «pochti» modelnoi kraevoi zadache dlya parabolicheskogo uravneniya vysokogo poryadka”, Differ. uravn., 23:1 (1987), 22–29 | MR | Zbl

[5] Baderko E. A., “O razreshimosti granichnykh zadach dlya parabolicheskikh uravnenii vysokogo poryadka v oblastyakh s krivolineinymi bokovymi granitsami”, Differ. uravn., 12:10 (1976), 1781–1792 | MR | Zbl

[6] Baderko E. A., “O reshenii pervoi kraevoi zadachi dlya parabolicheskikh uravnenii s pomoschyu potentsiala prostogo sloya”, Dokl. AN SSSR., 283:1 (1985), 11–13 | MR | Zbl

[7] Baderko E. A., “Reshenie zadachi s kosoi proizvodnoi dlya parabolicheskogo uravneniya metodom granichnykh integralnykh uravnenii”, Differ. uravn., 25:1 (1989), 14–20 | MR | Zbl

[8] Baderko E. A., Cherepova M. F., “Pervaya kraevaya zadacha dlya parabolicheskikh sistem v ploskikh oblastyakh s negladkimi bokovymi granitsami”, Dokl. RAN., 458:4 (2014), 379–381 | Zbl

[9] Baderko E. A., Cherepova M. F., “Potentsial prostogo sloya i pervaya kraevaya zadacha dlya parabolicheskoi sistemy na ploskosti”, Diffen. uravn., 52:2 (2016), 198–208

[10] Dzyadyk V. K., Vvedenie v teoriyu ravnomernogo priblizheniya funktsii polinomami., M., 1977 | MR

[11] Zeineddin M., “Gladkost potentsiala prostogo sloya dlya parabolicheskoi sistemy vtorogo poryadka v klassakh Dini”, Dep. VINITI RAN. — 16.04.92. — No 1294-V92.

[12] Kamynin L. I., “Gladkost teplovykh potentsialov v prostranstve Dini—Geldera”, Sib. mat. zh., 11:5 (1970), 1017–1045 | MR

[13] Kamynin L. I., “K teorii Zhevre dlya parabolicheskikh potentsialov, VI”, Differ. uravn., 8:6 (1972), 1015–1025 | MR | Zbl

[14] Kamynin L. I., “O reshenii metodom potentsialov osnovnykh kraevykh zadach dlya odnomernogo parabolicheskogo uravneniya vtorogo poryadka”, Sib. mat. zh., 1974:4, 806–834 | MR | Zbl

[15] Kamynin L. I., Khimchenko B. N., “Ob analogakh teoremy Zhiro dlya parabolicheskogo uravneniya 2-go poryadka”, Sib. mat. zh., 14:1 (1973), 86–110 | MR | Zbl

[16] Kamynin L. I., “Prilozhenie parabolicheskikh potentsialov Pani k kraevym zadacham matematicheskoi fiziki”, Differ. uravn., 26:5 (1990), 829–841 | MR | Zbl

[17] Tveritinov V. A., “Gladkost potentsiala prostogo sloya dlya parabolicheskoi sistemy vtorogo poryadka”, Dep. VINITI AN SSSR. — 02.09.88. — No 6850-V88.

[18] Tikhonov A. N., “O funktsionalnykh uravneniyakh tipa Volterra i ikh primeneniyakh k nekotorym zadacham matematicheskoi fiziki”, Byull. MGU. Sek. A., 1:8 (1938), 1–25

[19] Fridman A., Uravneniya s chastnymi proizvodnymi parabolicheskogo tipa, Mir, M., 1968

[20] Cherepova M. F., “O zadache Bitsadze—Samarskogo dlya parabolicheskogo uravneniya”, Vestn. Mosk. un-ta. Ser. 1. Mat. Mekh., 1986, no. 4, 74–76 | Zbl

[21] Sheveleva V. N., “Ob odnoi zadache kontaktnoi teploprovodnosti”, Differ. uravn., 27:1 (1991), 172–174 | MR | Zbl

[22] Sheveleva V. N., “Ob odnoi zadache kontaktnoi teploprovodnosti, II”, Differ. uravn., 28:4 (1992), 729–730 | MR | Zbl

[23] Baderko E. A., Cherepova M. F., “Bitsadze–Samarskii problem for parabolic systems with Dini continuous coefficients”, Compl. Var. Ellipt. Equ., 64:5 (2019), 753–765 | DOI | MR | Zbl