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## Limits of solutions to the singularly perturbed abstract hyperbolic-parabolic system

Authors: Andrei Perjan, Galina Rusu

### Abstract

We study the behavior of solutions to the problem $$\left\{ \begin{array}{l} \varepsilon u''_{\varepsilon}(t)+u'_{\varepsilon}(t)+ A(t)u _{\varepsilon}(t)=f_{\varepsilon}(t),\quad t \in (0,T), \\ u_{\varepsilon}(0)=u_{0\varepsilon},\quad u'_{\varepsilon}(0)=u_{1\varepsilon},\ \end{array} \right.$$ in the Hilbert space H as $\varepsilon\to0$, where $A(t), t \in (0,\infty),$ is a family of linear self-adjoint operators.

Department of Mathematics and Informatics
Moldova State University
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