On the phenomenon of the support shrinking of a solution with a time delay and on the extinction of the solution

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 de...

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Bibliographic Details
Published in:Sbornik. Mathematics 2021-02, Vol.212 (2), p.170-184
Main Author: Degtyarev, S. P.
Format: Article
Language:English
Subjects:
Diffusion rate
Time lag
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Summary: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.
ISSN:1064-5616
1468-4802
DOI:10.1070/SM9377