### Optimal feedback control in the problem of the motion of a viscoelastic fluid

DOI: http://dx.doi.org/10.12775/TMNA.2004.014

#### Abstract

We study an optimization problem for the feedback control system emerging

as a regularized model for the motion of a viscoelastic fluid subject

to the Jeffris-Oldroyd rheological relation. The approach includes systems

governed by the classical Navier-Stokes equation as a particular case.

Using the topological degree theory for condensing multimaps we prove

the solvability of the approximating problem and demonstrate the convergence

of approximate solutions to a solution of a regularized one. At last we show

the existence of a solution minimizing a given convex, lower semicontinuous

functional.

as a regularized model for the motion of a viscoelastic fluid subject

to the Jeffris-Oldroyd rheological relation. The approach includes systems

governed by the classical Navier-Stokes equation as a particular case.

Using the topological degree theory for condensing multimaps we prove

the solvability of the approximating problem and demonstrate the convergence

of approximate solutions to a solution of a regularized one. At last we show

the existence of a solution minimizing a given convex, lower semicontinuous

functional.

#### Keywords

Optimal control; feedback control; viscoelastic fluid; Navier-Stokes equation; Jeffris-Oldroyd rheological relation; topological degree; condensing multivalued map

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