Singularly perturbed Cauchy problem for abstract linear differential equations of second order in Hilbert spaces

We study the behavior of solutions to the problem
$$ \begin{cases} \varepsilon\bigl(u_\varepsilon''(t)+A_1u_\varepsilon(t)\bigr)+u_\varepsilon'(t)+A_0u_\varepsilon(t)=f(t), \quad t>0,\\ u_\varepsilon(0)=u_0, \quad u_\varepsilon'=u_1, \end{cases} $$
in the Hilbert space $H$ as $\varepsilon\mapsto 0$ where $A_1$ and $A_0$ are two linear selfadjoint operators.