An undamped wave equation, defined on a three-dimensional bounded domain \(\Omega\), which is coupled with a thermoelastic plate equation, whose dynamics is defined on a flat surface \(\Gamma_0\) of the boundary \(\Gamma\) of \(\Omega\), is considered.
The main result states that nonlinear boundary dissipation placed only on a suitable portion of the part of the boundary complementary to \(\Gamma_0\), suffices for the stabilization of the entire structure.
It provides “optimal” uniform decay rates for the energy functional corresponding to the full structure. These rates are described by a suitable nonlinear ordinary differential equation, whose coefficients depend on the growth of the nonlinear dissipation at the origin.