A Remark on Semilinear Perturbations of Abstract Parabolic Equations.

results are given which apply to semilinear parabolic equations. Simple examples are provided by initial-value problems for semilinear equation like u sub t = delta u + f(u). As applied to this situation, the results show that for suitable f and t greater than 0 the solution u(t,phi) of the problem with the initial-value phi varies continuously together with its space derivatives as phi varied in a weaker sense - e.g. small perturbations of phi in some L sub P-norms cause small changes in u(t,phi) in the space on continuously differentiable functions. (Author)