Exponential decay for the coupled Klein-Gordon-Schrödinger equations with locally distributed damping
Exponential decay for the coupled Klein-Gordon-Schrödinger equations with locally distributed damping
The following coupled damped Klein-Gordon-Schrödinger equations are considered $\begin{array}{l}i\psi t + \Delta \psi + i\alpha b(x){( - \Delta )^{\frac{1}{2}}}b(x)\psi = \phi \psi {\chi _\omega }\;{\rm{in}}\;\Omega \times (0,\infty ),(\alpha > 0)\\\phi tt - \Delta \phi + a(x)\phi t = {\left| \psi \right|^2}{\chi _\omega }\;{\rm{in}}\;\Omega \times (0,\infty ),\end{array}$ where $Ω$ is a …