## Uniform stabilization of the Euler-Bernoulli equation with feedback operator only in the Neumann boundary condition.(English)Zbl 0747.93070

Constantin Carathéodory: an international tribute. Vol. II, 1049-1074 (1991).
Summary: [For the entire collection see Zbl 0728.00004.]
We study the uniform stabilization problem for the Euler-Bernoulli equation defined in a smooth, bounded domain $$\Omega$$ of $$R^ n$$, with just one suitable dissipative boundary feedback operator acting on the Neumann B.C., while the Dirichlet B.C. is kept homogeneous. The uniform stabilization results which we present are fully consistent with recently established exact controllability and optimal regularity theories, which in fact motivate the choice of the function spaces in the first place. In particular, if the dissipative feedback operator acts on the entire boundary $$\Gamma$$, no geometrical conditions on $$\Omega$$ are needed.

### MSC:

 93D15 Stabilization of systems by feedback 93C20 Control/observation systems governed by partial differential equations

### Biographic References:

Carathéodory, Constantin

Zbl 0728.00004