Global Attractor of One Nonlinear Parabolic Equation

  • O. V. Kapustyan
  • D. V. Shkundin


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.
How to Cite
Kapustyan, O. V., and D. V. Shkundin. “Global Attractor of One Nonlinear Parabolic Equation”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 55, no. 4, Apr. 2003, pp. 446-55,
Research articles