Global Attractor of One Nonlinear Parabolic Equation - Kapustyan, O. V.; Shkundin, D. V. (Ukrains’kyi Matematychnyi Zhurnal, 2003)
We apply the theory of multivalued semiflows to a nonlinear parabolic equation of the “reaction–diffusion” type in the case where it is impossible to prove the uniqueness of its solution. A multivalued semiflow is generated by solutions satisfying a certain estimate global in time. We establish the existence of a global compact attractor in the phase space for the multivalued semiflow generated by a nonlinear parabolic equation. We prove that this attractor is an upper-semicontinuous function of a parameter.