ON NON-AUTONOMOUS CAUCHY PROBLEMS WITH OPERATOR MATRIC

Abstract

On the product space En, whereE is a Banach space we consider the Cauchy problem ˙ U(t)=A(t)U(t), 0 ≤t ≤T, U(s)=x ∈E , (0.1) where A(t)=( ai,j(t)A)n×n, D(A(t)) = [D(A)]n for an operator A on E and matrices (ai,j(t))n×n on C n. Then we apply the result to the linearized thermoelastic plate equations