Renormalized solutions for convection-diffusion problems involving a nonlocal operator

The aim of this paper is to establish an L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^1$$\end{document}-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.