On Polynomial Stability of Coupled Partial Differential Equations in 1D
arXiv:1911.06715 · doi:10.1007/978-3-030-46079-2_20
Abstract
We study the well-posedness and asymptotic behaviour of selected PDE-PDE and PDE-ODE systems on one-dimensional spatial domains, namely a boundary coupled wave-heat system and a wave equation with a dynamic boundary condition. We prove well-posedness of the models and derive rational decay rates for the energy using an approach where the coupled systems are formulated as feedback interconnections of impedance passive regular linear systems.
12 pages, 1 figure, accepted for publication in the Proceedings of "Semigroups of Operators: Theory and Applications", Kazimierz Dolny, Poland, October 2018