## Preprint 2013-21

## Erwan Hingant, Mauricio Sepúlveda:

### On a sorption-coagulation equation: statement, existence and numerical approximation

### Abstract:

This paper is devoted to the design and the mathematics of a new sorption-coagulation equation type, modeling interactions between metal ions and water-soluble polymers. We motivate a new brand model that accounts for the evolution of the configurational density of polymers and metal ions, which consists in a non-linear transport equation with a quadratic source term, the coagulation. A global in time existence result is established and a time explicit finite volume scheme for a conservative reformulation of the problem is proposed. Then, we prove a convergence result of the sequence of numerical approximation thanks to L1 - weak compactness arguments.