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On a mixed problem for a linear coupled system with variable coefficients. (English) Zbl 0886.35043
Summary: We prove existence, uniqueness, and exponential decay of solutions to the mixed problem $u''(x,t)-\mu(t)\Delta u(x,t)+\sum_{i=1}^n{\frac{\partial \theta}{\partial x_i}(x,t)}=0, \quad \theta'(x,t)-\Delta \theta(x,t) +\sum_{i=1}^n{\frac{\partial u'}{\partial x_i}(x,t)}=0,$ with a suitable boundary damping and a positive real-valued function $$\mu$$.

##### MSC:
 35F15 Boundary value problems for linear first-order PDEs 35N10 Overdetermined systems of PDEs with variable coefficients 35B40 Asymptotic behavior of solutions to PDEs
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