We will consider a system of PDEs that describes miscible displacement in porous media. If the initial and boundary conditions are such that a more viscous fluid displaces a less viscous fluid, their interface is unstable. Any small perturbation leads to viscous fingers. In practice, the following question plays an important role: is it possible to estimate the velocity of the fingers?
Time permitting, we will talk about the applications of these estimates in the optimal injection profile problem.