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.

中文翻译：

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涉及非局部算子的对流扩散问题的重整化解

本文的目的是在涉及非局部扩散算子的各向异性扩散对流问题的重归一化熵解的意义上建立\(L^1\) -适定性理论。我们的策略是遵循 Bendahmane 和 Karlsen (SIAM J Math Anal, 36(2):405–422, 2004) 开发的方法来概括 Karlsen 和 Ulusoy (J Differ Equ 116:1–23) 的存在性和唯一性结果, 2011) 到具有依赖于未知函数u的术语源的可积初始数据类。