This note shows how classical tools from linear control theory can be leveraged to provide a global analysis of nonlinear reaction–diffusion models. The approach is differential in nature. It proceeds contraction and recent extensions dissipativity.

The paper is devoted to the mathematical analysis of Cauchy problem for general cross-diffusion systems without any assumption about its entropic structure. A global existence result nonnegative solutions obtained by applying a classical Schauder fixed point theorem. proof upgraded enhancing regularity solution, namely gradient belongs space Lr((0,T)×Ω) some r>2. To this aim, Schauder's strateg...