TY - JOUR AU - ObukhovskiÄ­, Valeri AU - Zecca, Pietro AU - Zvyagin, Victor G. PY - 2004/06/01 Y2 - 2024/03/29 TI - Optimal feedback control in the problem of the motion of a viscoelastic fluid JF - Topological Methods in Nonlinear Analysis JA - TMNA VL - 23 IS - 2 SE - DO - UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2004.014 SP - 323 - 337 AB - We study an optimization problem for the feedback control system emergingas a regularized model for the motion of a viscoelastic fluid subjectto the Jeffris-Oldroyd rheological relation. The approach includes systemsgoverned by the classical Navier-Stokes equation as a particular case.Using the topological degree theory for condensing multimaps we provethe solvability of the approximating problem and demonstrate the convergenceof approximate solutions to a solution of a regularized one. At last we showthe existence of a solution minimizing a given convex, lower semicontinuousfunctional. ER -