完全非局部扩散方程的熵解

Pub Date : 2024-09-01 DOI:10.1002/mana.202400130

Ying Li, Chao Zhang

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引用次数: 0

摘要

我们考虑了具有非负数据的完全非局部扩散方程。基于近似和能量方法，我们证明了此类问题的非负熵解的存在性和唯一性。我们的结果尤其适用于时空分数拉普拉斯方程。

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Entropy solutions to the fully nonlocal diffusion equations

We consider the fully nonlocal diffusion equations with nonnegative $L^{1}$ -data. Based on the approximation and energy methods, we prove the existence and uniqueness of nonnegative entropy solutions for such problems. In particular, our results are valid for the time-space fractional Laplacian equations.

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