Strong stability of operator-differential equations and operator-difference schemes in integral norms with respect to time (Q1603185)

The paper deals the derivation of stability estimates under perturbations of an unbounded operator of the Cauchy problem for an abstract parabolic equation with the right-hand side and the initial condition in Hilbert spaces. The corresponding two-layer operator-difference schemes are considered from a similar viewpoint. A priori estimates for the perturbation error in integral norms with respect to time are derived because these estimates are very important in the study of well-posedness of problems with generalized solutions. The presented theory is illustrated by three examples.