Almost periodicity of inhomogeneous parabolic evolution equations
Lahcen Maniar, Roland Schnaubelt · 2019
We show the (asymptotic) almost periodicity of the bounded solution to the parabolic evolution equation u ′( t ) = A ( t ) u ( t ) + f ( t ) on ℝ (on ℝ + ) assuming that the linear operators A ( t ) satisfy the ‘Acquistapace–Terreni’ conditions, that the evolution family generated by A (·) has an exponential dichotomy, and that R ( ω, A (·)) and f are (asymptotically) almost periodic.