Kang-Sheng Liu

Sharp Damping Location for Stability of a Locally Damped Wave Equation and its Galerkin Approximation

We study the stability of the variable coefficient wave equation $u_{tt}-u_{xx}-(1+x^{2})u_{yy}+\chi_{\mathbb G}u_{t}=0$ on the rectangle $(-1,1)\times(0,\pi)$ with Dirichlet boundary conditions, where the viscous damping acts on a vertical strip $\mathbb G=(\eta-\delta,\eta+\delta)\times(0,\pi)$. We establish a precis...