Perturbations of evolution equations

Abstract

One aspect of this study is to identify sets of initial conditions for which unique solutions for (1) and (2) exist. If solutions for (1) and (2) exist, both map (O, ∞) into the Banach space X and the convergence, with respect to some norm in X, of the solution of (1) to that of (2) as € tends to zero, is feasible. As Y and Y need not necessarily be the same, another aspect of the study is to identify initial values y€ € Y€ for (1) and y € Y for (2) such that the above convergence can be established.