## On a mixed problem for a linear coupled system with variable coefficients

### Summary

Summary: We prove existence, uniqueness and exponential decay of solutions to the mixed problem $$u''(x,t)-\mu(t)\Delta u(x,t)+\sum_{i=1}^n {\partial \theta\over\partial x_i}(x,t)=0   \theta'(x,t)-\Delta \theta(x,t) +\sum_{i=1}^n {\partial u'\over\partial x_i}(x,t)=0\,, with a suitable boundary damping, and a positive real-valued function \mu.$$

### Mathematics Subject Classification

35F15, 35N10, 35B40

### Keywords/Phrases

mixed problem, boundary damping, exponential stability