The global attractor of a dissipative nonlinear evolution system
The paper deals with long-time behaviour of dynamical systems generated by a dissipative nonlinear evolution system given by strongly coupled parabolic equations. To this end the authors study global classical solutions using a priori estimate technique. Moreover they prove uniqueness theorems, which allow them to define semigroups corresponding to the systems of parabolic equations mentioned above. Under some natural conditions on nonlinearities the authors prove the existence of a global attractor, and its regular properties.
scientific article; zbMATH DE number 1354754