论文标题
分数交叉扩散系统的推导作为由Lévy噪声驱动的随机多粒子系统的极限
Derivation of a Fractional Cross-Diffusion System as the Limit of a Stochastic Many-Particle System Driven by Lévy Noise
论文作者
论文摘要
在本文中，将分数交叉扩散系统得出作为由Lévy噪声驱动的中等相互作用粒子的多物种系统的严格多粒子极限。相互作用的形式是由带有分数电势压力的多孔培养基方程激励的。我们的方法基于Oelschläger（1989）和Stevens（2000）开发的技术，在后者中，显示了经验度量的正则化与相应正则化的宏观系统解决方案的正则化的收敛性。适当的结果和溶液的非阴性证明了正规宏观系统，然后在极限下对非调节分数交叉扩散系统产生相同的结果。
In this article a fractional cross-diffusion system is derived as the rigorous many-particle limit of a multi-species system of moderately interacting particles that is driven by Lévy noise. The form of the mutual interaction is motivated by the porous medium equation with fractional potential pressure. Our approach is based on the techniques developed by Oelschläger (1989) and Stevens (2000), in the latter of which the convergence of a regularization of the empirical measure to the solution of a correspondingly regularized macroscopic system is shown. A well-posedness result and the non-negativity of solutions are proved for the regularized macroscopic system, which then yields the same results for the non-regularized fractional cross-diffusion system in the limit.
