Document Type
Article
Publication Date
2017
DOI
10.1051/cocv/2015043
Publication Title
ESAIM: Control Optimisation and Calculus of Variations
Volume
23
Issue
1
Pages
137-164
Abstract
The Poisson-Nernst-Planck system of equations used to model ionic transport is interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of probability measures with finite second moment. A variational scheme is then set up and is the starting point of the construction of global weak solutions in a unified framework for the cases of both linear and non-linear diffusion. The proof of the main results relies on the derivation of additional estimates based on the flow interchange technique developed by Matthes et al. in [D. Matthes, R.J. McCann and G. Savare, Commun. Partial Differ. Equ. 34 (2009) 1352-1397].
Original Publication Citation
Kinderlehrer, D., Monsaingeon, L., & Xu, X. (2017). A Wasserstein gradient flow approach to Poisson-Nernst-Planck equations. ESAIM: Control Optimisation and Calculus of Variations, 23(1), 137-164. doi:10.1051/cocv/2015043
Repository Citation
Kinderlehrer, David; Monsaingeon, Leinard; and Xu, Xiang, "A Wasserstein Gradient Flow Approach to Poisson-Nernst-Planck Equations" (2017). Mathematics & Statistics Faculty Publications. 3.
https://digitalcommons.odu.edu/mathstat_fac_pubs/3