Clark, H.R.; San Gil Jutuca, L.P.; Milla Miranda, M.

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

Electron. J. Differ. Equ. 1998, Paper 4, 20 p. (1998)


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


mixed problem, boundary damping, exponential stability