Parabolic Differential Equations with Bounded Delay

Marek Kryspin, Janusz Mierczyński

Published 2022-07-18Version 1

We show the continuous dependence of solutions of linear nonautonomous second order parabolic partial differential equations (PDEs) with bounded delay on coefficients and delay. The assumptions are very weak: only convergence in the weak-* topology of delay coefficients is required. The results are important in the applications of the theory of Lyapunov exponents to the investigation of PDEs with delay.