The strong stability of a semigroup arising from a coupled hyperbolic/parabolic system
We consider here a coupled system of hyperbolic and parabolic PDE's which arises in a given fluid/structure interaction. The system is transformed into an abstract differential equation, and from this operator theoretic model, questions of strong stability for the equation are addressed. A distinctive feature of the problem is that the resolvent of the operator is not compact, and hence a treatment with the standard Nagy-Foias theory or the Lasalle Invariance Principle is not available. Instead, we show that a powerful stability result of Arendt-Batty applies, and which consequently proves strong decay of the energy functional. © 1998 Springer-Verlag New York Inc.
Avalos, G., & Lasiecka, I. (1998). The strong stability of a semigroup arising from a coupled hyperbolic/parabolic system. Semigroup Forum, 57 (2), 278-292. https://doi.org/10.1007/PL00005977