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Pré-Publication, Document De Travail Année : 2015

On systems of continuity equations with nonlinear diffusion and nonlocal drifts

Résumé

This paper is devoted to existence and uniqueness results for classes of nonlinear diffusion equations (or systems) which may be viewed as regular perturbations of Wasserstein gradient flows. First, in the case where the drift is a gradient (in the physical space), we obtain existence by a semi-implicit Jordan-Kinderlehrer-Otto scheme. Then, in the nonpotential case, we derive existence from a regularization procedure and parabolic energy estimates. We also address the uniqueness issue by a displacement convexity argument.
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Dates et versions

hal-01147666 , version 1 (05-06-2015)

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  • HAL Id : hal-01147666 , version 1

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Guillaume Carlier, Maxime Laborde. On systems of continuity equations with nonlinear diffusion and nonlocal drifts. 2015. ⟨hal-01147666⟩
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