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Anisotropic Degenerate Parabolic Problems in \(\mathbb {R}^N\) with Variable Exponent and Locally Integrable Data

  • Fares MokhtariEmail author
  • Rabah Mecheter
Article
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Abstract

In this paper, we prove the existence and regularity of weak solutions for a class of nonlinear anisotropic parabolic equations in the whole \((0,T)\times \mathbb {R}^N\) with \(p_i(x)\) growth conditions and locally integrable data. The functional setting involves Lebesgue–Sobolev spaces with variable exponents. Our results are generalizations of the corresponding results in the constant exponent case and some results given in Bendahmane et al. (Commun Pure Appl Anal 12:1201–1220, 2013).

Keywords

Variable exponents nonlinear parabolic equations anisotropic equations unbounded domain \( L^1_ {loc}\) data 

Mathematics Subject Classification

35K55 35K65 

Notes

Acknowledgements

The authors would like to thank the referees for their comments and suggestions.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics and InformaticsUniversity of Benyoucef BenkheddaAlgiersAlgeria
  2. 2.Laboratory of PDEENS-KoubaKoubaAlgeria
  3. 3.Department of Mathematics and InformaticsUniversity of Med BOUDIAFM’SilaAlgeria

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