Asymptotic Properties of Solutions of Nonautonomous Evolution Equations
by
Frank Raebiger
University of Tuebingen, Germany

We connect asymptotic properties of the solutions of the nonautonomous evolution equation

u'(t) = A(t) u(t) + f(t)

(NE)

on the Banach space X with spectral properties of the operator -[ d/dt] + A(t) considered on an appropriate space F(R, X) of X-valued functions. In particular, we characterize when (NE) has a unique solution belonging to the space C_b(R, X), C₀(R, X), P_q(R, X), and AP(R, X), respectively, provided that the inhomogeneity f is in the same space.

Date received: April 30, 1999