Parabolic evolution equations with asymptotically autonomous delay

Roland Schnaubelt
2003 Transactions of the American Mathematical Society  
We study retarded parabolic non-autonomous evolution equations whose coefficients converge as t → ∞, such that the autonomous problem in the limit has an exponential dichotomy. Then the non-autonomous problem inherits the exponential dichotomy, and the solution of the inhomogeneous equation tends to the stationary solution at infinity. We use a generalized characteristic equation to deduce the exponential dichotomy and new representation formulas for the solution of the inhomogeneous equation.
doi:10.1090/s0002-9947-03-03512-8 fatcat:h2qrtcemtbgp3gqs4o4nxnzfy4