An optimal Liouville-type theorem for radial entire solutions of the porous medium equation with source

DOI10.1016/j.jde.2008.10.018zbMath1172.35038OpenAlexW2058929262MaRDI QIDQ1018393

Philippe Souplet

Publication date: 19 May 2009

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2008.10.018

zbMATH Keywords

porous medium equationnonnegative weak solutionsBernstein-type estimatesbounded radial solutionsparabolic Liouville-type theorem

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Degenerate parabolic equations (35K65)

Related Items (9)

An optimal Liouville theorem for the porous medium equation ⋮ Optimal Liouville type theorems for porous medium systems with sources ⋮ Liouville-type theorem for a nonlinear sub-elliptic system involving \(\Delta_{\lambda}\)-Laplacian and advection terms ⋮ High-order weighted compact nonlinear scheme for solving degenerate parabolic equations ⋮ Liouville-type theorem for one-dimensional porous medium systems with sources ⋮ A universal bound for radial solutions of the quasilinear parabolic equation with \(p\)-Laplace operator ⋮ Liouville-type theorems for nonlinear degenerate parabolic equation ⋮ An optimal Liouville-type theorem of the quasilinear parabolic equation with a \(p\)-Laplace operator ⋮ On the finite time blow-up for filtration problems with nonlinear reaction

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