On the entropic structure of reaction-cross diffusion systems
  This paper is devoted to the study of systems of reaction-cross diffusion equations arising in population dynamics. New results of existence of weak solutions are presented, allowing to treat systems of two equations in which one of the cross diffusions is convex, while the other one is concave. The treatment of such cases involves a general study of the structure of Lyapunov functionals for cross diffusion systems, and the introduction of a new scheme of approximation, which provides simplified proofs of existence. 
Laurent Desvillettes, Thomas Lepoutre, Ayman Moussa, Ariane Trescases
math.AP