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Boundary stabilisation of the wave equation in the presence of singularities. (English) Zbl 1390.93630

Summary: We study the boundary stabilization of the wave equation by a nonlinear feedback active on a part of the boundary in geometric situations for which the solutions have singularities. These singularities appear at the interfaces at which the mixed Neumann-Dirichlet boundary conditions meet. Under a simple geometrical condition concerning the orientation of the boundary, we obtain sharp energy decay rates under a general growth assumption on the feedback. We show that the singularities do not affect the energy decay rates and give examples.

MSC:

93D15 Stabilization of systems by feedback
35L05 Wave equation
35Q53 KdV equations (Korteweg-de Vries equations)
93C20 Control/observation systems governed by partial differential equations
93C10 Nonlinear systems in control theory
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