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arXiv · 1310.3677

Gradient flows driven by a non-smooth repulsive interaction potential

Giovanni A. Bonaschi
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Abstract

This thesis analyze the Wasserstein gradient flow of a functional defined as a double convolution of a non-smooth repulsive interaction potential. To be more precise, the potential under investigation has a -|x| behavior close to the origin. The already existent machinery of Wasserstein gradient flow is well posed for lambda-convex potential. In this case this property is lost, but it is proven that in the one dimensional case existence and uniqueness of the solution is still achieved.

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Giovanni A. Bonaschi. 2013-10-14. Gradient flows driven by a non-smooth repulsive interaction potential. https://arxiv.org/abs/1310.3677

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