Differential and Integral Equations

Local and global boundedness for some nonlinear parabolic equations exhibiting a time singularity

Eurica Henriques and Rojbin Laleoglu

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Results on the local and global boundedness of nonnegative weak subsolutions of the doubly nonlinear parabolic equation $$ (u^{q})_t-\text{div}\,{(|\nabla u|^{p-2}\nabla u)}=0, $$ are obtained for $p > 1$ and $0 < q < 1$, that is, for equations presenting a singularity in the time derivative part (as well as a singularity, $1 < p < 2$, or degeneracy, $p > 2$, in the principal part of the operator). We work in measure spaces equipped with a doubling non-trivial Borel measure supporting a Poincaré inequality.

Article information

Differential Integral Equations, Volume 29, Number 11/12 (2016), 1029-1048.

First available in Project Euclid: 13 October 2016

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35B50: Maximum principles 35K65: Degenerate parabolic equations 35K67: Singular parabolic equations 35K20: Initial-boundary value problems for second-order parabolic equations


Henriques, Eurica; Laleoglu, Rojbin. Local and global boundedness for some nonlinear parabolic equations exhibiting a time singularity. Differential Integral Equations 29 (2016), no. 11/12, 1029--1048. https://projecteuclid.org/euclid.die/1476369328

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