论文标题
无界域上聚集扩散方程的确定粒子近似
Deterministic particle approximation of aggregation-diffusion equations on unbounded domains
论文作者
论文摘要
我们考虑一个一维聚集 - 扩散方程，它是功能上具有竞争吸引力的抑制相互作用的功能性的Wasserstein空间中的梯度流。 我们证明，在〜\ cite {di francesco-rosini}中引入的分段恒定密度的完全确定性粒子近似从一般有限的初始密度开始，以$ l^1 $在$ l^1 $中汇聚到PDE的有界弱解决方案。 In particular, the result is achieved in unbounded domains and for arbitrary nonnegative bounded initial densities, thus extending the results in \cite{Gosse-Toscani, Matthes-Osberger, Mathes-Soellner} (in which a no-vacuum condition is required) and giving an alternative approach to \cite{Carrillo-Craig-Patacchini} in the one-dimensional case, including also次级和超第二扩散。
We consider a one-dimensional aggregation-diffusion equation, which is the gradient flow in the Wasserstein space of a functional with competing attractive-repulsive interactions. We prove that the fully deterministic particle approximations with piecewise constant densities introduced in~\cite{Di Francesco-Rosini} starting from general bounded initial densities converge strongly in $L^1$ to bounded weak solutions of the PDE. In particular, the result is achieved in unbounded domains and for arbitrary nonnegative bounded initial densities, thus extending the results in \cite{Gosse-Toscani, Matthes-Osberger, Mathes-Soellner} (in which a no-vacuum condition is required) and giving an alternative approach to \cite{Carrillo-Craig-Patacchini} in the one-dimensional case, including also subquadratic and superquadratic diffusions.
