Аннотация:
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.
Ключевые слова и фразы:Singular perturbations, Cauchy problem, boundary function.