A splitting method for nonlinear diffusions with nonlocal, nonpotential drifts

Abstract : We prove an existence result for nonlinear diffusion equations in the presence of a nonlocal density-dependent drift which is not necessarily potential. The proof is constructive and based on the Helmholtz decomposition of the drift and a splitting scheme. The splitting scheme combines transport steps by the divergence-free part of the drift and semi-implicit minimization steps à la Jordan-Kinderlherer Otto to deal with the potential part.
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https://hal.archives-ouvertes.fr/hal-01332356
Contributor : Maxime Laborde <>
Submitted on : Wednesday, June 15, 2016 - 4:41:00 PM
Last modification on : Thursday, April 26, 2018 - 10:28:46 AM

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Guillaume Carlier, Maxime Laborde. A splitting method for nonlinear diffusions with nonlocal, nonpotential drifts. 2016. ⟨hal-01332356⟩

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