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Adaptive stabilization for a Kirchhoff-type nonlinear beam under boundary output feedback control. (English) Zbl 1107.35088
The authors consider a Kirchhoff-type nonlinear beam system with one end fixed and boundary control force applied at the other end. Using a constructive Galerkin approximation scheme, the existence and uniqueness of the classical solution for the system is proved. Then by an energy multiplier method, the exponential stability that is dependent on initial data is shown.

MSC:
35L75 Higher-order nonlinear hyperbolic equations
35B35 Stability in context of PDEs
93D15 Stabilization of systems by feedback
35L35 Initial-boundary value problems for higher-order hyperbolic equations
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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