梯度流型宏观人群运动模型
A macroscopic crowd motion model of gradient flow type
摘要：
一个简单的模型来处理在紧急疏散情况下的人流被认为是：在每一个点x，速度U（x），在x的个人希望实现的是给定的。然而，不可压缩性约束阻止了这一速度场的实现，实际速度是所需速度在容许速度集上的投影。而不是看一个微观的设置（其中个人代表刚性光盘），在这里的宏观方法进行了调查，其中未知的是密度的演变。如果给定一个梯度结构，比如说U是D的梯度的反方向，其中D是，例如，到出口门的距离，问题被表示为概率测度的Wasserstein空间中的梯度流。给出梯度流的泛函既不是定值的（因为它考虑了密度的约束），也不是测地线凸的，这需要对离散格式的收敛性进行专门研究。
英文摘要：
A simple model to handle the flow of people in emergency evacuation situations is considered: at every point x, the velocity U(x) that individuals at x would like to realize is given. Yet, the incompressibility constraint prevents this velocity field to be realized and the actual velocity is the projection of the desired one onto the set of admissible velocities. Instead of looking at a microscopic setting (where individuals are represented by rigid discs), here the macroscopic approach is investigated, where the unknwon is the evolution of the density . If a gradient structure is given, say U is the opposite of the gradient of D where D is, for instance, the distance to the exit door, the problem is presented as a Gradient Flow in the Wasserstein space of probability measures. The functional which gives the Gradient Flow is neither finitely valued (since it takes into account the constraints on the density), nor geodesically convex, which requires for an ad-hoc study of the convergence of a discrete scheme.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
