Decay rates of interactive hyperbolic-parabolic PDE models with thermal effects on the interface
This study focuses on coupled PDE systems comprising of a hyperbolic and a parabolic-like equation with an interface on a portion of the boundary. The main issue addressed is that of uniform stability of the overall interactive model. The main observation states that boundary nonlinear dissipation placed only on a suitable portion of the part of the boundary suffices for the stabilization of the entire structure.
Applied Mathematics and Optimization
Lasiecka, I., & Lebiedzik, C. (2000). Decay rates of interactive hyperbolic-parabolic PDE models with thermal effects on the interface. Applied Mathematics and Optimization, 42 (2), 127-167. https://doi.org/10.1007/s002450010010