In this article we deal with a class of degenerate parabolic systems which exhibit two phenomena: porous medium effects and chemotaxis ones. Such classes of equations arise in the modelling (on the mesoscale) of biomass spreading mechanisms via chemotaxis. Under certain "balance conditions'' on the order of the porous medium degeneracy and the growth of the chemotactic functions, we prove well posedness.
"On the well posedness of a class of PDEs including porous medium and chemotaxis effect." Adv. Differential Equations 16 (9/10) 937 - 954, September/October 2011.