CONTINUOUS DEPENDENCE RESULTS FOR PARABOLIC PROBLEMS WITH TIME-DEPENDENT COEFFICIENTS

Abstract

We prove continuous dependence results for parabolic problems in which the coefficients and boundary conditions depend on both space and time. Using semi-groups and fundamental solutions, together with a priori estimates for elliptic boundary value problems, we obtain continuous dependence results with respect to changes in the coefficients of the differential and boundary operators, as well as in the initial conditions.