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.
Biography
Graduated from Faculty of Mathematics and Mechanics of V. N. Karazin Kharkov National University in 1993 (department of mathematical physics). Ph.D. thesis was defended in 1999.
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.
Grigory M. Sklyar, Alexander V. Rezounenko, “Strong asymptotic stability and constructing of stabilizing controls”, Mat. Fiz. Anal. Geom., 10:4 (2003), 569–582
Alexander Rezounenko, “On singular limit dynamics for a class of retarded nonlinear partial differential equations”, Mat. Fiz. Anal. Geom., 4:1/2 (1997), 193–211
I. D. Chueshov, A. V. Rezounenko, “Global attractors for a class of retgirded quasilinear partial differential equations”, Mat. Fiz. Anal. Geom., 2:3 (1995), 363–383
