Parabolic differential equations with bounded delay

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.

Automated summary

This paper demonstrates the continuous dependence of solutions of linear nonautonomous second-order parabolic partial differential equations (PDEs) with bounded delay on coefficients and delay. The assumptions made in this study are very weak, only requiring convergence in the weak-* topology of delay coefficients. The results are important for the application of Lyapunov exponents theory in investigating PDEs with delay.