On a Mixed Problem for a Linear Coupled System with Variable Coefficients

Abstract

We prove existence, uniqueness and exponential decay of solutions to the mixed problem u" (x,t) - μ(t)Δu(x,t) + Σn i=1 ∂θ/∂xi (x,t) = 0, θ' (x,t) - Δθ(x,t) + Σn i=1 ∂u'/∂xi (x,t) = 0, with a suitable boundary damping, and a positive real-valued function μ.