DOI: 10.1007/s002450010010 Appl Math Optim 42:127–167 (2000) © 2000 Springer-Verlag New York Inc. Decay Rates of Interactive Hyperbolic-Parabolic PDE Models with Thermal Effects on the Interface ∗ I. Lasiecka and C. Lebiedzik Department of Mathematics, Kerchof Hall, University of Virginia, Charlottesville,VA 22903, USA Abstract. We consider coupled PDE systems comprising of a hyperbolic and a parabolic-like equation with an interface on a portion of the boundary. These mod- els are motivated by structural acoustic problems. A specific prototype consists of a wave equation defined on a three-dimensional bounded domain  coupled with a thermoelastic plate equation defined on Ŵ 0 —a flat surface of the bound- ary ∂. Thus, the coupling between the wave and the plate takes place on the interface Ŵ 0 . The main issue studied here is that of uniform stability of the overall interactive model. Since the original (uncontrolled) model is only strongly stable, but not uniformly stable, the question becomes: what is the “minimal amount” of dissipation necessary to obtain uniform decay rates for the energy of the overall system? Our main result states that boundary nonlinear dissipation placed only on a suitable portion of the part of the boundary which is complementary to Ŵ 0 , suf- fices for the stabilization of the entire structure. This result is new with respect to the literature on several accounts: (i) thermoelasticity is accounted for in the plate model; (ii) the plate model does not account for any type of mechanical damping, including the structural damping most often considered in the literature; (iii) there is no mechanical damping placed on the interface Ŵ 0 ; (iv) the boundary damping is nonlinear without a prescribed growth rate at the origin; (v) the un- damped portions of the boundary ∂ are subject to Neumann (rather than Dirichlet) boundary conditions, which is a recognized difficulty in the context of stabilization of wave equations, due to the fact that the strong Lopatinski condition does not hold. ∗ This work was partially supported by NSF Grant DMS-9804056 and ARO Grant DAAH04-96-1-0099.