Geodesic
Examples of the Nonuniqueness of Solutions of the Mixed Problem for the Heat Equation in Unbounded Domains
Matematičeskie zametki, Tome 91 (2012) no. 1, pp. 67-73.

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For a wide class of domains of revolution, we construct examples of the nonuniqueness of solutions of the first mixed problem for the heat equation, which supports the exactness of a uniqueness class of Täcklind type.
Keywords: heat equation, Cauchy problem, uniqueness class of Täcklind type, measurable function, Hilbert space, Harnack's inequality.
Mots-clés : domain of revolution 
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L. M. Kozhevnikova. Examples of the Nonuniqueness of Solutions of the Mixed Problem for the Heat Equation in Unbounded Domains. Matematičeskie zametki, Tome 91 (2012) no. 1, pp. 67-73. http://geodesic.mathdoc.fr/item/MZM_2012_91_1_a5/

[1] E. Holmgren, “Sur les solutions quasi analytiques de l'équation de la chaleur”, Ark. Mat. Astron. Fys., 18:9 (1924) | Zbl

[2] A. Tychonoff, “Théorèmes d'unicité pour l'équation de la chaleur”, Matem. sb., 42:2 (1935), 199–216 | Zbl

[3] S. Täcklind, “Sur les class quasianalytiques des solutions des equations aux deriveés partielles du type parabolique”, Nova Acta Reg. Soc. Schi. Uppsal. Ser. 4, 10:3 (1936), 3–55

[4] O. A. Ladyzhenskaya, “O edinstvennosti resheniya zadachi Koshi dlya lineinogo parabolicheskogo uravneniya”, Matem. sb., 27:2 (1950), 175–184 | MR | Zbl

[5] O. A. Oleinik, E. V. Radkevich, “Metod vvedeniya parametra dlya issledovaniya evolyutsionnykh uravnenii”, UMN, 33:5 (1978), 7–76 | MR | Zbl

[6] A. G. Gagnidze, “O edinstvennosti reshenii kraevykh zadach v neogranichennykh oblastyakh dlya parabolicheskikh uravnenii”, Tr. sem. im. I. G. Petrovskogo, 13, Izd-vo Mosk. un-ta, M., 1988, 123–126 | MR | Zbl

[7] A. K. Guschin, “O ravnomernoi stabilizatsii reshenii vtoroi smeshannoi zadachi dlya parabolicheskogo uravneniya”, Matem. sb., 119:4 (1982), 451–508 | MR | Zbl

[8] F. Kh. Mukminov, “O ravnomernoi stabilizatsii reshenii pervoi smeshannoi zadachi dlya parabolicheskogo uravneniya”, Matem. sb., 181:11 (1990), 1486–1509 | MR | Zbl

[9] L. M. Kozhevnikova, “Klassy edinstvennosti reshenii pervoi smeshannoi zadachi dlya uravneniya $u_t=Au$ c kvaziellipticheskim operatorom $A$ v neogranichennykh oblastyakh”, Matem. sb., 198:1 (2007), 59–102 | MR | Zbl

[10] J. Moser, “A Harnack inequality for parabolic differential equations”, Comm. Pure Appl. Math., 17:1 (1964), 101–134 | DOI | MR | Zbl

[11] O. A. Ladyzhenskaya, V. A. Solonnikov, N. N. Uraltseva, Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967 | MR | Zbl