Nonlocal Interaction Equations in Environments with Heterogeneities and Boundaries
Nonlocal Interaction Equations in Environments with Heterogeneities and Boundaries
复制标题
具有异质性和边界的环境中的非局部相互作用方程
DOI：
10.1080/03605302.2015.1015033
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发表时间：
2015
影响因子：
1.9
通讯作者：
D. Slepčev
中科院分区：
文献类型：
--
作者：
Lijiang Wu;D. Slepčev
研究了一类具有空间依赖迁移率的非局部相互作用方程的适定性。我们也考虑到边界和外部潜力的存在。在此基础上，研究了具有黎曼度量g的l - d的子集上的非局部相互作用方程。得到了相互作用势与几何的关系条件，证明了解的存在性、唯一性和稳定性。研究了具有riemanian 2-Wasserstein度规的系统在概率测度空间中梯度流动的方程组。
We study well-posedness of a class of nonlocal interaction equations with spatially dependent mobility. We also allow for the presence of boundaries and external potentials. Such systems lead to the study of nonlocal interaction equations on subsets ℳ of ℝ d endowed with a Riemannian metric g. We obtain conditions, relating the interaction potential and the geometry, which imply existence, uniqueness and stability of solutions. We study the equations in the setting of gradient flows in the space of probability measures on ℳ endowed with Riemannian 2-Wasserstein metric.
影响因子：
2.5
作者：
Balague, D.;Carrillo, J. A.;Raoul, G.
通讯作者：
Raoul, G.