On the strong stability of first-order operator-differential equations (Q2387940)

The authors present a construction of a priori strong stability estimates for the Cauchy problem of an abstract first-order linear differential equation in a Hilbert space under perturbations with respect to the initial condition and the right-hand side. They prove that a priori strong stability estimates may be deduced directly on the basis of various a priori estimates for the solution of the Cauchy problem.