Blow-up to a $p$-Laplacian parabolic equation with a general nonlinear source

Hang Ding; Jun Zhou

doi:10.5802/crmeca.248

Article de recherche

Blow-up to a

p

-Laplacian parabolic equation with a general nonlinear source
[effondrement d’une équation parabolique

p

-laplacienne avec une source non-linéaire générale]

Hang Ding ¹ ; Jun Zhou ¹

¹ School of Mathematics and Statistics, Southwest University, Chongqing, 400715, P.R.China

Comptes Rendus. Mécanique, Volume 352 (2024), pp. 71-80.

Résumé
Abstract

Une équation parabolique $p$ -laplacienne avec un terme source non linéaire général est considérée. On montre que la solution peut exploser en temps fini pour une énergie initiale positive. De plus, sous certaines hypothèses appropriées concernant le terme source non linéaire, il est prouvé que la solution explose en temps fini pour une énergie initiale arbitrairement élevée. Ces résultats généralisent des résultats antérieurs.

A $p$ -Laplacian parabolic equation with a general nonlinear source term is considered. It is shown that the solution may blow up in finite time at positive initial energy. Moreover, under some suitable assumptions about the nonlinear source term, the solution is proved to blow up in finite time at arbitrarily high initial energy. These results generalize the previous ones.

Reçu le : 2023-04-17
Révisé le : 2024-03-05
Accepté le : 2024-03-07
Publié le : 2024-04-04

DOI : 10.5802/crmeca.248

Classification : 35K92, 35B44
Keywords: $p$-Laplacian parabolic equation, general nonlinear source term, blow-up
Mot clés : équation parabolique $p$-laplacienne, terme source non linéaire général, explosion

Affiliations des auteurs :

Hang Ding ¹ ; Jun Zhou ¹

¹ School of Mathematics and Statistics, Southwest University, Chongqing, 400715, P.R.China

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Hang Ding and Jun Zhou},
     title = {Blow-up to a $p${-Laplacian} parabolic equation with a general nonlinear source},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {71--80},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {352},
     year = {2024},
     doi = {10.5802/crmeca.248},
     language = {en},
}

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Hang Ding; Jun Zhou. Blow-up to a $p$-Laplacian parabolic equation with a general nonlinear source. Comptes Rendus. Mécanique, Volume 352 (2024), pp. 71-80. doi : 10.5802/crmeca.248. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.248/

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