Destruction of the family of steady states in the planar problem of   Darcy convection
  The natural convection of incompressible fluid in a porous medium causes for some boundary conditions a strong non-uniqueness in the form of a continuous family of steady states. We are interested in the situation when these boundary conditions are violated. The resulting destruction of the family of steady states is studied via computer experiments based on a mimetic finite-difference approach. Convection in a rectangular enclosure is considered under different perturbations of boundary conditions (heat sources, infiltration). Two scenario of the family of equilibria are found: the transformation to a limit cycle and the formation of isolated convective patterns. 
V.G. Tsybulin, B. Karas\"ozen