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Renormalized solutions for convection-diffusion problems involving a nonlocal operator

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Abstract

The aim of this paper is to establish an \(L^1\)-well-posedness theory in the sense of renormalized entropy solution for anisotropic diffusion-convection problems involving a nonlocal diffusion operator. Our strategy is to follow the approach developed in Bendahmane and Karlsen (SIAM J Math Anal, 36(2):405–422, 2004) to generalize the existence and the uniqueness results of Karlsen and Ulusoy (J Differ Equ 116:1–23, 2011) to the class of integrable initial data with a term source depending on the unknown function u.

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Acknowledgements

We thank Boris ANDREIANOV for his encouraging advises and helpful criticism. We are also grateful to him for his kind remarks and suggestions which contributed to improve this paper.

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Authors and Affiliations

  1. Département de Mathématiques, Université Nazi Boni (UNB), 01 BP 1091 Bobo 01, Bobo-Dioulasso, Burkina Faso

    Adama Ouédraogo & Idrissa Ibrango

  2. Laboratoire de Mathématiques, d’Informatique et Applications (LaMIA), Université Nazi Boni (UNB), 01 BP 1091 Bobo 01, Bobo-Dioulasso, Burkina Faso

    Dofyniwassouani Alain Houede

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  1. Adama Ouédraogo
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  2. Dofyniwassouani Alain Houede
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  3. Idrissa Ibrango
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Correspondence to Adama Ouédraogo.

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The first author gratefully dedicates the present work to Professor Hamidou TOURÉ.

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Ouédraogo, A., Houede, D.A. & Ibrango, I. Renormalized solutions for convection-diffusion problems involving a nonlocal operator. Nonlinear Differ. Equ. Appl. 28, 55 (2021). https://doi.org/10.1007/s00030-021-00713-8

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