论文标题
在曲率有界曲率的Riemannian歧管上相互作用模型的长期行为
Long-time behaviour of interaction models on Riemannian manifolds with bounded curvature
论文作者
论文摘要
我们研究了在有界截面曲率的平滑riemannian歧管上对非局部部分微分方程的长期行为。方程模拟具有固有相互作用的自然化行为，这些行为是由相互作用潜力建模的。我们认为有吸引力的相互作用潜力，并为共识状态建立足够的条件，以渐近地形成。此外，我们通过得出溶液支撑直径的收敛速率来量化共识方法。分析结果由旋转组设置的方程式的数值模拟支持。
We investigate the long-time behaviour of solutions to a nonlocal partial differential equation on smooth Riemannian manifolds of bounded sectional curvature. The equation models self-collective behaviour with intrinsic interactions that are modelled by an interaction potential. We consider attractive interaction potentials and establish sufficient conditions for a consensus state to form asymptotically. In addition, we quantify the approach to consensus, by deriving a convergence rate for the diameter of the solution's support. The analytical results are supported by numerical simulations for the equation set up on the rotation group.
