一类具有熵结构的交叉扩散系统有界解的偏 Hölder 正则性
偏微分方程分析
2021-12-30 v2
摘要
在本文中,我们获得了一类交叉扩散系统有界解的偏 正则性,该类系统是强耦合的退化拟线性抛物系统。在稍更强的假设下,我们得到偏 正则性。我们所考虑的交叉扩散系统具有形式梯度流结构,即它们在形式上等同于某个凸熵泛函的梯度流。此外,我们假设交叉扩散系统不是体积填充的。我们在本文中引入的主要新工具是“粘合熵密度”,它使我们能够在这种新设定下仿效 Giaquinta 和 Struwe 关于非线性抛物系统偏 Hölder 正则性的经典理论。为展示我们结果的适用性,我们给出两个满足我们假设且已被充分研究的交叉扩散系统例子——其中之一是用于种群动力学的双组分 Shigesada-Kawasaki-Teramoto (SKT) 模型。
引用
@article{arxiv.2007.03561,
title = {Partial H\"{o}lder Regularity for Bounded Solutions of a Class of Cross-Diffusion Systems with Entropy Structure},
author = {Marcel Braukhoff and Claudia Raithel and Nicola Zamponi},
journal= {arXiv preprint arXiv:2007.03561},
year = {2021}
}
备注
Merged into new submission, "Partial Holder Regularity for Solutions of a Class of Cross-Diffusion Systems with Entropy Structure", with substantially broader scope. This submission only included non volume-filling models, such as the Shigesada-Kawasaki-Teramoto model, whereas the new preprint can also handle volume-filling models, such as the Maxwell-Stefan model