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IMCS/Publications/BASM/Issues/BASM n.3 (76), 2014/

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
A.Mateevici str. 60, MD 2009, Chisinau
Moldova
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