Resurgence flows in porous media.

Porous media with resurgences can be described by a double structure, namely, a continuous porous medium and capillaries with impermeable walls which relate distant points of the continuous medium. The resurgences can be either punctual or extended. The equations for flow in such media are derived; some general properties of the resulting system, which involves nonlocal aspects, are deduced. A "dilute" approximation is detailed for punctual resurgences in two-dimensional media and is illustrated by a few examples.