On the existence of solutions for a strongly degenerate system
María Teresa González Montesinos, Francisco Ortegón Gallego · Comptes Rendus Mathématique · 2006
We establish the existence of a solution in a certain sense to a strongly degenerate problem consisting in a coupled nonlinear parabolic-elliptic system. The diffusion term in the parabolic equation is of the form − div a ( x , t , u , ∇ u ) , where a is an operator of the Leray–Lions type. Moreover, the second equation is nonuniformly elliptic.