Artykuł  

Degenerate singular parabolic problems with natural growth

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creativeworkseries.issn1232-9274
dc.contributor.authorEl Ouardy, Mounim
dc.contributor.authorEl Hadfi, Youssef
dc.contributor.authorSbai, Abdelaaziz
dc.date.issued2024
dc.description.abstractIn this paper, we study the existence and regularity results for nonlinear singular parabolic problems with a natural growth gradient term $\$ \begin{cases}\frac{\partial u}{\partial t}-\operatorname{div}((a(x,t)+u^{q})|\nabla u|^{p-2}\nabla u)+d(x,t)\frac{|\nabla u|^{p}}{u^{\gamma}}=f & \text{ in } Q,\\ u(x,t)=0 & \text{ on } \Gamma, \\ u(x,t=0)=u_{0}(x) & \text{ in } \Omega, \end{cases} \$$ where $\Omega$ is a bounded open subset of $\mathbb{R}^{N}$, $N\gt 2$, $Q$ is the cylinder $\Omega \times (0,T)$, $T\gt 0$, $\Gamma$ the lateral surface $\partial \Omega \times (0,T)$, $2\leq p\lt N$, $a(x,t)$ and $b(x,t)$ are positive measurable bounded functions, $q\geq 0$, $0\leq\gamma\lt 1$, and $f$ non-negative function belongs to the Lebesgue space $L^{m}(Q)$ with $m\gt 1$, and $u_{0}\in L^{\infty}(\Omega)$ such that $\$\forall\omega\subset\subset\Omega\, \exists D_{\omega}\gt 0:\, u_{0}\geq D_{\omega}\text{ in }\omega.\$$ More precisely, we study the interaction between the term $u^{q}$ $(q>0)$ and the singular lower order term $d(x,t)|\nabla u|^{p}u^{-\gamma}$ $(0\lt\gamma\lt 1)$ in order to get a solution to the above problem. The regularizing effect of the term $u^q$ on the regularity of the solution and its gradient is also analyzed.en
dc.description.placeOfPublicationKraków
dc.description.versionwersja wydawnicza
dc.identifier.doihttps://doi.org/10.7494/OpMath.2024.44.4.471
dc.identifier.eissn2300-6919
dc.identifier.issn1232-9274
dc.identifier.urihttps://repo.agh.edu.pl/handle/AGH/108411
dc.language.isoeng
dc.publisherWydawnictwa AGH
dc.rightsAttribution 4.0 International
dc.rights.accessotwarty dostęp
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/legalcode
dc.subjectdegenerate parabolic equationsen
dc.subjectsingular parabolic equationsen
dc.subjectnatural growth termen
dc.titleDegenerate singular parabolic problems with natural growthen
dc.title.relatedOpuscula Mathematica
dc.typeartykuł
dspace.entity.typePublication
publicationissue.issueNumberNo. 4
publicationissue.paginationpp. 471-503
publicationvolume.volumeNumberVol. 44
relation.isJournalIssueOfPublication958a565f-0ba8-4db5-bbd6-a87484b6015d
relation.isJournalIssueOfPublication.latestForDiscovery958a565f-0ba8-4db5-bbd6-a87484b6015d
relation.isJournalOfPublication304b3b9b-59b9-4830-9178-93a77e6afbc7
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