Asymptotic stability conjecture for wave equations with positive-real impedance

Let $\hat{z}$ be the impedance introduced earlier, and let the Cauchy problem be the multidimensional wave equation with the associated impedance boundary condition. Assume that $\hat{z}$ is positive-real, meaning that its real part is nonnegative in the relevant right half-plane, and has no isolated singularities on $i\mathbb{R}$. Asymptotic stability conjecture. The Cauchy problem is asymptotically stable in a suitable energy space. The conjecture proposes a unified asymptotic-stability result for wave equations coupled with physically motivated positive-real impedance boundary conditions; the paper establishes stability for several important classes, while the stated general case remains open.