一般交叉扩散系统的大时间渐近行为及新型凸Sobolev不等式
Large-time asymptotics for general cross-diffusion systems and novel convex Sobolev inequalities
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中文总结 AI 辅助
本文研究一般交叉扩散系统弱解向常数稳态的指数衰减，利用相对熵方法并引入新型凸Sobolev不等式，推广了现有结果至更广参数范围。
中文摘要 AI 辅助
研究了有界域中无通量边界条件下一般交叉扩散系统的弱解向常数稳态的指数衰减。定量衰减率的证明基于相对熵方法，涉及两个参数：决定熵密度的指数和熵产生积分中的指数。关键要素是新型凸Sobolev不等式，这些不等式将文献中现有结果推广到这两个参数的广泛取值范围。这些不等式通过凸性论证和Gagliardo-Nirenberg不等式建立。
英文摘要
The exponential decay of weak solutions towards the constant steady state of general cross-diffusion systems in bounded domains with no-flux boundary conditions is investigated. The proof of quantitative decay rates is based on the relative entropy method and involves two parameters: the exponent determining the entropy density and the exponent in the entropy production integral. The key ingredient are novel convex Sobolev inequalities, which extend existing results in the literature to a broad range of values of the two parameters. These inequalities are established using convexity arguments and the Gagliardo-Nirenberg inequality.
发表机构
- TU Wien（维也纳工业大学）
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