仿射Darken类Maxwell-Stefan扩散系统的全局强解
Global Strong Solutions for the Affine Darken Class of Maxwell-Stefan Diffusion Systems
- Technische Universität Darmstadt（达姆施塔特工业大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该论文证明仿射Darken类Maxwell-Stefan扩散系统在无小性假设下具有全局极大L^p强适定性，并给出通量形式、熵对称化及指数收敛等性质。
AI中文摘要：
Bothe和Druet的核心对角闭包将多组分Darken扩散识别为热力学一致的Maxwell-Stefan模型，其中本构数据为物种示踪扩散率。基于我们近期预印本中为加性Maxwell-Stefan摩擦引入的Stieltjes坐标和De Giorgi正则性框架，我们证明了仿射Darken类在无小性假设下，对具有成分依赖标量系数和一致正示踪扩散率的全局极大L^p强适定性。我们表明这恰好是保持全局论证所依据的固定Stieltjes特征框架的最大Darken类。对于一般光滑、一致正的Darken示踪扩散率，我们还推导了直接约束通量形式、精确混合熵对称化、Fisher耗散、成分一致正规椭圆性以及局部强适定性。仿射类中的解保持与单纯形边界一致分离，在正时间变为经典解，并指数收敛到平衡态。常数乘性摩擦（包括重复因子）通过将具有相等因子的物种分组来覆盖。
英文摘要：
The core-diagonal closure of Bothe and Druet identifies multicomponent Darken diffusion as a thermodynamically consistent Maxwell-Stefan model in which the constitutive data are species tracer diffusivities. Building on the Stieltjes-coordinate and De Giorgi regularity framework introduced in our recent preprint for additive Maxwell-Stefan frictions, we prove global maximal-$L^p$ strong well-posedness, without smallness assumptions, for the affine Darken class with composition-dependent scalar coefficients and uniformly positive tracer diffusivities. We show that this is exactly the maximal Darken class preserving the fixed Stieltjes eigenframe underlying the global argument. For general smooth, uniformly positive Darken tracer diffusivities we also derive the direct constrained flux form, exact mixing-entropy symmetrization, Fisher dissipation, composition-uniform normal ellipticity, and local strong well-posedness. Solutions in the affine class remain uniformly separated from the simplex boundary, become classical for positive times, and converge exponentially to equilibrium. Constant multiplicative frictions, including repeated factors, are covered by grouping species with equal factors.
