ON NON-AUTONOMOUS CAUCHY PROBLEMS WITH OPERATOR MATRICES

Nguyen Thanh Lan

Abstract


On the product space E^n, where E is a Banach space we consider the Cauchy problem
U'(t)=A(t)U(t), 0?t?T,
U(s)=x \in E,
where A(t)=(a_{i,j}(t)A){n}, D(A(t)) = [D(A)]^n for an operator A on E and matrices (a_{i,j}(t))_{n} on C^n. Then we apply the result to the linearized thermoelastic plate equations.

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