This paper concerns with the smoothness of bounded solutions for semilinear evolution equations in Banach spaces. The smoothness of bounded solutions for such equations is proved without assuming that the semigroup is analytic and compactness. We just use the representation of the bounded solution as an improper integral from minus infinity to t and a result about closed operators in Banach spaces. As a preliminaries, we prove the existence and the stability of these bounded solutions, the uniqueness in some cases and the almost periodicity under additional conditions. To prove the existence, we use the Banach fixed point theorem. Finally, we apply this result to the strongly damped wave equation.

smoothness bounded solutions, evolutions equations, wave equation.