Abstract:
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, domain of revolution, Hilbert space, Harnack's inequality.
Citation:
L. M. Kozhevnikova, “Examples of the Nonuniqueness of Solutions of the Mixed Problem for the Heat Equation in Unbounded Domains”, Mat. Zametki, 91:1 (2012), 67–73; Math. Notes, 91:1 (2012), 58–64
\Bibitem{Koz12}
\by L.~M.~Kozhevnikova
\paper Examples of the Nonuniqueness of Solutions of the Mixed Problem for the Heat Equation in Unbounded Domains
\jour Mat. Zametki
\yr 2012
\vol 91
\issue 1
\pages 67--73
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\transl
\jour Math. Notes
\yr 2012
\vol 91
\issue 1
\pages 58--64
\crossref{https://doi.org/10.1134/S0001434612010063}
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Linking options:
https://www.mathnet.ru/eng/mzm8582
https://doi.org/10.4213/mzm8582
https://www.mathnet.ru/eng/mzm/v91/i1/p67
This publication is cited in the following 3 articles:
M. M. Amangalieva, M. T. Dzhenaliev, M. T. Kosmakova, M. I. Ramazanov, “On one homogeneous problem for the heat equation in an infinite angular domain”, Siberian Math. J., 56:6 (2015), 982–995
M. H. Jenaliyev, M. Amangaliyeva, M. Kosmakova, M. Ramazanov, “About Dirichlet boundary value problem for the heat equation in the infinite angular domain”, Bound. Value Probl., 2014 (2014), 213, 21 pp.