- Global finite-energy well-posedness is proved for a semilinear wave-diffusion system with mixed Dirichlet-Neumann boundary conditions.
- Dissipation acts only through the diffusion component; stabilization of the wave is therefore indirect.
- High-frequency wave eigenvalues satisfy Re(s_n) = -kappa^2/(2 lambda_n) + O(lambda_n^{-3/2}), ruling out exponential stability.
- A sharp resolvent estimate ||(i omega-A)^{-1}|| = O(|omega|^2) yields the optimal strong-data energy decay E(t)=O(t^{-1}).
- Small semilinear perturbations inherit arbitrarily near-sharp polynomial decay near the equilibrium.
