Loading...
Please wait, while we are loading the content...
Similar Documents
Equivalence of gradient flows and entropy solutions for singular nonlocal interaction equations in 1
| Content Provider | Semantic Scholar |
|---|---|
| Author | Bonaschi, G. A. Carrillo, José A. Francesco, Marco Di Peletier, Mark A. |
| Copyright Year | 2013 |
| Abstract | We prove the equivalence between the notion of Wasserstein gradient flow for a onedimensional nonlocal transport PDE with attractive/repulsive Newtonian potential on one side, and the notion of entropy solution of a Burgers-type scalar conservation law on the other. The solution of the former is obtained by spatially differentiating the solution of the latter. The proof uses an intermediate step, namely the L2 gradient flow of the pseudo-inverse distribution function of the gradient flow solution. We use this equivalence to provide a rigorous particle-system approximation to the Wasserstein gradient flow, avoiding the regularization effect due to the singularity in the repulsive kernel. The abstract particle method relies on the so-called wave-front-tracking algorithm for scalar conservation laws. Finally, we provide a characterization of the sub-differential of the functional involved in the Wasserstein gradient flow. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://pure.tue.nl/ws/files/3944508/21275206488336.pdf |
| Alternate Webpage(s) | http://people.bath.ac.uk/mdf29/BonCarDifPel_Submitted.pdf |
| Alternate Webpage(s) | http://www.win.tue.nl/analysis/reports/rana13-25.pdf |
| Alternate Webpage(s) | http://people.disim.univaq.it/~mdifrance/BCDP_arXiv.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Aharonov–Bohm effect Algorithm Approximation Flow Gradient Nonlocal Lagrangian Particle system Pseudo brand of pseudoephedrine Singular Solutions Technological singularity Turing completeness |
| Content Type | Text |
| Resource Type | Article |
