Stabilization of the wave equation with acoustic and delay boundary conditions
The paper is devoted to analysis of the well-posedness and stability property of the wave equation with acoustic boundary conditions and boundary delay. The structure of the paper is as follows. First, the author writes the considered equation in the form of abstract first order evolution equation. Then, it is proved that the operator of this equation generates a strongly continuous semigroup in a corresponding space. Using known results by Lasiecka et al., the author establishes sufficient conditions of stability for the equation with delay in the wave component. The exponential decay of the energy functional is also proved. Finally, the author establishes the sufficient conditions of stability for the equation with delay in the oscillator component.
scientific article; zbMATH DE number 6893040
scientific article