ALMOST AUTOMORPHIC MILD SOLUTIONS OF HYPERBOLIC EVOLUTION EQUATIONS WITH STEPANOV-LIKE ALMOST AUTOMORPHIC FORCING TERM

This article concerns the existence and uniqueness of almost automorphic solutions to the semilinear parabolic boundary differential equations x'(t) A(m)x(t) + f(t, x(t)), t is an element of R, Lx(t) = phi(t, x(t)), t is an element of R, where A := A(m vertical bar ker) (L) generates a hyperbolic analytic semigroup on a Banach space X, with Stepanov-like almost automorphic nonlinear term, defined on some extrapolated space X alpha-1, for 0 < alpha < 1 and phi takes values in the boundary space delta X.