Systems of parabolic equations with delays: Continuous dependence on parameters

Abstract

Results on continuous dependence on parameters, as well as on regularization, of solutions to linear systems of parabolic partial differential equations of second order with delay are given. One of the main features is that the topology on the zero order and delay coefficients is the weak-* topology on an $L_{\infty}$ space, whereas the assumptions on the second- and first-order coefficients are slightly stronger. This is important in the context of generation of linear skew-product dynamical systems by such equations.