一般交叉扩散系统的改进弱-强唯一性
Improved weak-strong uniqueness for general cross-diffusion systems
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中文总结 AI 辅助
本文针对含/不含体积填充效应、含/不含完全强制性的一般交叉扩散系统，建立有界解的弱-强唯一性，通过构造粘合熵、利用梯度估计与Gagliardo-Nirenberg不等式放宽假设，将分析扩展至非强制性系统，弥补强制性缺失。
中文摘要 AI 辅助
针对一大类交叉扩散系统（含或不含体积填充效应、含或不含完全强制性），本文建立了有界解的弱-强唯一性。与现有结果相比，强解的正则性和正定性假设被显著放宽。该分析还可扩展至非强制性系统，体积填充约束可弥补强制性的缺失。证明基于两个核心思路：通过构造粘合熵消除正定性条件，利用梯度估计和Gagliardo-Nirenberg不等式放宽正则性要求。
英文摘要
The weak-strong uniqueness of bounded solutions is established for a broad class of cross-diffusion systems, with or without volume-filling effects, and with or without full coercivity. Compared to existing results, the regularity and positivity assumptions on the strong solution are significantly relaxed. The analysis also extends to non-coercive systems, with the volume-filling constraint compensating for the lack of coercivity. The proof is based on two key ideas: The positivity condition is eliminated through the construction of a glued entropy, while the regularity requirement can be relaxed by using the gradient estimate and the Gagliardo-Nirenberg inequality.
