Abstract
The first boundary value problem with zero boundary values is considered for a one-dimensional linear parabolic equation. If the equation is sufficiently close to the heat equation, the rate of decreasing for the solution is connected with the number of zero level lines of the solution, nonvanishing for all values of time. Bibliography: 4 titles.
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Literature Cited
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T.D. Wentzel,Asymptotic behavior of solutions of the heat equation in domains with a curvilinear boundary, Tr. Sem. Imeni Petrovskogo14 (1989), 57–65.
Additional information
Translated from Trudy Seminara imeni I.G. Petrovskogo, No. 17, pp. 118–127, 1994.
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Wentzel, T.D. On the decay rate of solutions of linear parabolic equations for infinitely increasing time. J Math Sci 75, 1691–1697 (1995). https://doi.org/10.1007/BF02368670
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DOI: https://doi.org/10.1007/BF02368670