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

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• 作者：M. Mabdaoui ; H. Moussa ; M. Rhoudaf
• 关键词：Non ; linear parabolic problems ; Orlicz–Sobolev spaces ; Entropy solutions ; Lower order term ; Truncation
• 刊名：Analysis and Mathematical Physics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：7
• 期：1
• 页码：47-76
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Analysis; Mathematical Methods in Physics;
• 出版者：Springer International Publishing
• ISSN：1664-235X
• 卷排序：7

文摘

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 \(L^1(Q_T)\).KeywordsNon-linear parabolic problemsOrlicz–Sobolev spaces Entropy solutionsLower order termTruncationReferences1.Adams, R.: Sobolev spaces. Academic Press, New York (1975)MATHGoogle Scholar2.Azroul, E., Redwane, H., Rhoudaf, M.: Existence of a renormalized solution for a class of nonlinear parabolic equations in Orlicz Spaces. Port. Math. 66(1), 29–63 (2009)MathSciNetCrossRefMATHGoogle Scholar3.Ben Cheikh Ali, M., Guibé, O.: Nonlinear and non-coercive elliptic problems with integrable data (English summary). Adv. Math. 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