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Ricerche di Matematica

, Volume 68, Issue 2, pp 745–767 | Cite as

Renormalized solutions to nonlinear parabolic problems with blowing up coefficients and general measure data

  • Mohammed AbdellaouiEmail author
  • Elhoussine Azroul
Article

Abstract

An existence result is established for a class of quasilinear parabolic problem which is a diffusion type equations having continuous coefficients blowing up for a finite value of the unknown, a second hand \(\mu \in \mathcal {M}_{b}(Q)\) and an initial data \(u_{0}\in L^{1}(\Omega )\). We develop a technique which relies on the notion of a renormalized solution and an adequate regularization in time for certain truncation functions. Some compactness results are also shown under additional hypotheses.

Keywords

Nonlinear parabolic equations Blowing-up coefficients Renormalized solutions Radon measures 

Résumé

Un résultat d’existenece est établi pour une classe de problèmes paraboliques quasilinéaires sous forme d’équations de type diffusion à coefficients continues qui explosent pour une valeur finie du variable, la deuxième partie \(\mu \in \mathcal {M}_{b}(Q)\) et la donnée initiale \(u_{0}\in L^{1}(\Omega )\). Nous developpons une technique basée sur la notion de solution renormalisée et une régularisation adéquate en temps pour certaines fonctions troncatures. Quelques résultas de compacité sont aussi démontrés sous des hypthèses supplémentaires.

Mathematics Subject Classification

35R05 35B45 41A30 32U20 28A33 

Notes

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Copyright information

© Università degli Studi di Napoli "Federico II" 2019

Authors and Affiliations

  1. 1.Laboratory LAMA, Department of Mathematics, Faculty of Sciences Dhar El MahrazUniversity of FezAtlas FezMorocco

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