Nonlinear Diffusion: Geodesic Convexity is Equivalent to Wasserstein Contraction
Nonlinear Diffusion: Geodesic Convexity is Equivalent to Wasserstein Contraction
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非线性扩散：测地线凸性等同于 Wasserstein 收缩
DOI：
10.1080/03605302.2014.892987
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发表时间：
2014
影响因子：
1.9
通讯作者：
Bolley F
中科院分区：
文献类型：
--
作者：
Bolley F
众所周知，非线性扩散方程可以解释为具有欧几里德-瓦瑟斯坦距离的概率测度空间中的梯度流。在适当的凸性条件下，由于McCann的非线性，相关的熵是测地凸的，这意味着所有解之间关于这个距离的压缩类型的性质。在这篇注记中，我们给出了一个简单而直接的证明，证明了这种压缩型性质和这种凸性条件之间的等价性，而不需要借助熵和梯度流结构。
It is well known that nonlinear diffusion equations can be interpreted as a gradient flow in the space of probability measures equipped with the Euclidean Wasserstein distance. Under suitable convexity conditions on the nonlinearity, due to McCann , the associated entropy is geodesically convex, which implies a contraction type property between all solutions with respect to this distance. In this note, we give a simple straightforward proof of the equivalence between this contraction type property and this convexity condition, without even resorting to the entropy and the gradient flow structure.
影响因子：
0.8
作者：
A. Lytchak
通讯作者：
A. Lytchak