The existence of a finite-dimensional global attractor for a class of retarded partial differential equations is proved. The methods of inertial manifolds and inertial manifolds with delay are extended to the case of retarded semilinear parabolic equations.
Main publications:
Chueshov I. D., Rezounenko A. V. Global attractors for a class of retarded quasilinear partial differential equations // C. R. Acad. Sci. Paris. Ser. I. 1995. No. 321. P. 607–612.
Boutet de Monvel L., Chueshov I. D., Rezounenko A. V. Long-time behaviour of strong solutions for a class of retarded nonlinear P. D. E. s // Communications in Partial Differential Equations. 1997. No. 22(9,10). P. 1453–1474.
Boutet de Monvel L., Chueshov I. D., Rezounenko A. V. Inertial manifolds for retarded semilinear parabolic equations // Nonlinear Analysis. 1998. No. 34. P. 907–925.
Rezounenko A. V. Inertial Manifolds with Delay for Retarded Semilinear Parabolic Equations // Discrete and Continuous Dynamical Systems. 2000., V. 6, No. 4. P. 829–840.
