Global existence results for near triangular nonlinear parabolic systems

In this thesis, we propose and prove the sufficient conditions which ensure the global existence of weak solutions for two classes of nonlinear parabolic systems with cross diffusion. The first class is the triangular system and the second is close to the first kind in some sense, i.e the near triangular system. First, we prove technical lemmas, the so-called decay estimates, which are necessary for main results as well as interesting in themselves. Then we prove that weak solutions of the mentioned systems belong to proper Campanato spaces. Finally, the isomorphism theorem among Campanato and Holder spaces allows us to establish the Holder regularity of these solutions. By Amann's results, this regularity guarantees the global existence of weak solutions.