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arXiv · 1606.04793

A splitting method for nonlinear diffusions with nonlocal, nonpotential drifts

Guillaume Carlier·Maxime Laborde
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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 \`a la Jordan-Kinderlherer-Otto to deal with the potential part.

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Guillaume Carlier, Maxime Laborde. 2016-06-15. A splitting method for nonlinear diffusions with nonlocal, nonpotential drifts. https://arxiv.org/abs/1606.04793

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