On a Miscible Displacement Model in Porous Media Flow with Measure Data
Jérôme Droniou, Kyle S. Talbot · SIAM Journal on Mathematical Analysis · 2014
We establish the existence of a solution to a nonlinearly coupled elliptic-parabolic system of PDEs describing the single-phase, miscible displacement of one incompressible fluid by another in a porous medium. We consider a velocity-dependent diffusion-dispersion tensor and model the action of injection and production wells by measures on the domain. We obtain the solution by passing to the limit on problems with regularized well data.