I want to ask two questions about the stabilization of the equation \begin{aligned} & {y_{tt}} = k {y_{xx}}+a {y_t}+ b {y_x}+c y , \quad (t,x) \in {\text{ }}(0,\infty ) \times (0 ,1) \\ & y(t,0) = y(t,1) = 0 \\ & y(x,0) = f(x)\\ & y_t(x,0) = g(x) \end{aligned} where the coefficients $k$, $a$, $b$, $c$ are functions of $(t,x)$.
- Is there exists an exponential stabilization result concerning the above equation?
- Is there a physical interpretation of the stabilization of such an equation? Or it is just mathematics?