Some remarks on quasilinear parabolic problems with singular potential and a reaction term
type: Item
instance of: scholarly article
title: Some remarks on quasilinear parabolic problems with singular potential and a reaction term
zbMATH Open document ID: 1297.35118
author: Boumediene Abdellaoui
author: Sofiane El-Hadi Miri
author: Ireneo Peral
author: Tarik Mohamed Touaoula
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 2014-09-05T00:00:00Z
review text: The authors consider the following quasilinear parabolic equation \[ (u^{\theta})_t - \Delta_pu = \lambda\frac{u^{p-1}|}{|x|^p} + u^q + f(x,t), \] where \(\theta\) is either 1 or \(p-1\), \(N\geq3\), \(\Omega\) is either a bounded regular domain containing the origin or \(\Omega\) is equal to all the space, \(1<p<N\), \(q>0\) and \(f\geq 0\) with suitable hypotheses. Such kind of problems are related to the classical Hardy inequality. The authors obtain natural conditions to show the existence or the nonexistence of nonnegative solutions. In the case of nonexistence result, the authors analyse blow-up phenomena for approximated problems in connection with a strong maximum principle and with the Harnack inequality. They also study when finite time extinction (\(1<p<2\)) and finite speed propagation (\(p>2\)) occur giving sharp conditions on the reaction power.
reviewed by: Vincenzo Vespri
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K59
Mathematics Subject Classification ID: 35B44
zbMATH DE Number: 6340663
zbMATH Keywords: Hardy potential
zbMATH Keywords: Harnack inequality
zbMATH Keywords: finite time extinction
zbMATH Keywords: finite speed propagation
MaRDI profile type: Publication
full work available at URL: s00030-013-0253-y
OpenAlex ID: W2022455442
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DOI: 10.1007/S00030-013-0253-Y
description: scientific article; zbMATH DE number 6340663