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Sbornik: Mathematics, 2021, Volume 212, Issue 2, Pages 170–184
DOI: https://doi.org/10.1070/SM9377 (Mi sm9377) 		 
On the phenomenon of the support shrinking of a solution with a time delay and on the extinction of the solution

S. P. Degtyarev

Institute of Applied Mathematics and Mechanics, Donetsk, Ukraine
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DOI: https://doi.org/10.1070/SM9377
Abstract: The phenomenon of support shrinking with a time delay for the solution of a doubly nonlinear degenerate parabolic equation is studied in the case of slow diffusion and strong absorption. For a nonnegative solution, a sufficient condition for support shrinking beginning with some moment of time is deduced in terms of the local behaviour of the mass of the initial datum. It is also proved that the solution vanishes identically in finite time.
Bibliography: 21 titles.
Keywords: degenerate parabolic equation, absorption, support shrinking, extinction of a solution.
Received: 04.02.2020 and 12.07.2020
Russian version:
Matematicheskii Sbornik, 2021, Volume 212, Number 2, Pages 38–52
DOI: https://doi.org/10.4213/sm9377
Bibliographic databases:
Document Type: Article
UDC: 517.956.45+517.956.8
MSC: Primary 35K55; Secondary 35K65, 35B40
Language: English
Original paper language: Russian
Citation: S. P. Degtyarev, “On the phenomenon of the support shrinking of a solution with a time delay and on the extinction of the solution”, Mat. Sb., 212:2 (2021), 38–52; Sb. Math., 212:2 (2021), 170–184
Citation in format AMSBIB
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    References:34
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