TY - JOUR
AU - O. V. Kapustyan
AU - D. V. Shkundin
PY - 2003/04/25
Y2 - 2024/11/14
TI - Global Attractor of One Nonlinear Parabolic Equation
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 55
IS - 4
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/3918
AB - 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.
ER -