Periodic waves in unsaturated porous media with hysteresis
  We consider a PDE system with degenerate hysteresis describing unsaturated flow in 3D porous media. Assuming that a time periodic forcing is prescribed on the boundary, we prove that a time periodic response exists as long as the amplitude of the forcing terms is small enough to keep the solution within the convexity domain of the hysteresis operator. 
B. Albers, P. Krejci, E. Rocca
math.AP