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The paper concerned with higher order asymptotic expansion of solutions tothe Cauchy problem of abstract hyperbolic equations of the form $u''+Au+u'=0$in a Hilbert space, where $A$ is a nonnegative selfadjoint operator. The resultsays that by assuming the regularity of initial data, asymptotic profiles (ofarbitrary order) are explicitly written by using the semigroup $e^{-tA}$generated by $-A$. To prove this, a kind of maximal regularity for $e^{-tA}$ isused.

Higher order asymptotic expansion of solutions to abstract linear hyperbolic equations