Conditions for the uniform well-posedness of the Cauchy problem for an equation with variable operator in a Hilbert space (Q1100417)

From author's introduction: Let H be a Hilbert space, A(t) a linear operator whose domain \(D(A)=D(A(t))\) is dense in H and does not depend on t \((0\leq t\leq T<\infty)\). Consider the equation (1): \(dx/dt=A(t)x.\) In the paper there are obtained necessary and sufficient conditions of uniform well-posedness of the Cauchy problem for the equation (1). At the same time, the corresponding result for the equation with a constant operator is generalized and the well known Kato's theorem for the variable operator (which is valid for every Banach space) is regained - in case of Hilbert space - in stronger form.