Lack of smoothing for bounded solutions of a semilinear parabolic equation

We study a semilinear parabolic equation that possesses global bounded weak solutions whose gradient has a singularity in the interior of the domain for all > 0. The singularity of these solutions is of the same type as the singularity of a stationary solution to which they converge as → ∞.

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Bibliographic Details
Published in:Advances in nonlinear analysis 2020-03, Vol.9 (1), p.1437-1452
Main Authors: Fila, Marek, Lankeit, Johannes
Format: Article
Language:English
Subjects:
35B44
35K58
semilinear parabolic equation
singular gradient
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Description
Summary:We study a semilinear parabolic equation that possesses global bounded weak solutions whose gradient has a singularity in the interior of the domain for all > 0. The singularity of these solutions is of the same type as the singularity of a stationary solution to which they converge as → ∞.
ISSN:2191-9496
2191-950X
DOI:10.1515/anona-2020-0059