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Oblique projection local feedback stabilization of nonautonomous semilinear damped wave-like equations. (English) Zbl 1443.93102

The authors study the stabilization of a class of nonlinear weakly damped wave equations by means of a finite-dimensional feedback control. The stabilizing control is constructed based on an appropriate oblique projection and it enters as a time-dependent linear combination of a finite number of suitable indicator functions supported in small regions. Numerical experiments are given for validate the theoretical results.

MSC:

93D15 Stabilization of systems by feedback
93D23 Exponential stability
93C20 Control/observation systems governed by partial differential equations
35L05 Wave equation
35L71 Second-order semilinear hyperbolic equations
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