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Entropy solutions for a nonlinear parabolic problems with lower order term in Orlicz spaces

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Abstract

We shall give the proof of existence results for the entropy solutions of the following nonlinear parabolic problem

where A is a Leray–Lions operator having a growth not necessarily of polynomial type. The lower order term \(\Phi \) :\(\Omega \times (0,T)\times \mathbb {R}\rightarrow \mathbb {R}^N\) is a Carathéodory function, for a.e. \((x,t)\in Q_T\) and for all \(s\in \mathbb {R}\), satisfying only a growth condition and the right hand side f belongs to \(L^1(Q_T)\).

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Authors and Affiliations

  1. Département de Mathématiques, Faculté des Sciences et Techniques de Tanger, B.P. 416, Tangier, Morocco

    M. Mabdaoui

  2. Département de Mathématiques et Informatique, Faculté des Sciences Meknès, BP 11201, Zitoune, Meknes, Morocco

    H. Moussa & M. Rhoudaf

Authors
  1. M. Mabdaoui
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  2. H. Moussa
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  3. M. Rhoudaf
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Correspondence to H. Moussa.

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Mabdaoui, M., Moussa, H. & Rhoudaf, M. Entropy solutions for a nonlinear parabolic problems with lower order term in Orlicz spaces. Anal.Math.Phys. 7, 47–76 (2017). https://doi.org/10.1007/s13324-016-0129-5

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  • DOI: https://doi.org/10.1007/s13324-016-0129-5

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