Abstract
We consider an initial and boundary value problem the one dimensional wave equation with damping concentrated at an interior point. We prove a result of a logarithmic decay of the energy of a system with homogeneous Dirichlet boundary conditions. The method used is based on the resolvent estimate approach which derives from the Carleman estimate technique. Under an algebraic assumption describing the right location of the actuator, we prove a logarithmic decay of the energy of solution. We show that this assumption is lower than the one given by 20 and 1 which depends on the diophantine approximations properties of the actuator's location.
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Schedule a callMore From: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
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