Global Attractor of One Nonlinear Parabolic Equation
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.
English version (Springer): Ukrainian Mathematical Journal 55 (2003), no. 4, pp 535-547.
Citation Example: Kapustyan O. V., Shkundin D. V. Global Attractor of One Nonlinear Parabolic Equation // Ukr. Mat. Zh. - 2003. - 55, № 4. - pp. 446-455.