Pollution Transfer as Optimal Mass Transport Problem


  •  L. Ndiaye    
  •  Mb. Ndiaye    
  •  A. Sy    
  •  D. Seck    

Abstract

In this paper, we use mass transportation theory to study pollution  transfer in  porous media.  We show   the existence of a $L^2-$regular vector field defined by a $W^{1, 1}-$ optimal transport map. A sufficient condition for solvability of our model, is given by   a (non homogeneous) transport equation with  a  source defined by a measure. The mathematical framework used, allows us to  show in some specifical cases, existence of solution for  a nonlinear PDE deriving from the modelling. And we end by numerical simulations.


This work is licensed under a Creative Commons Attribution 4.0 License.