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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2014, Number 3, Pages 49–64
(Mi basm371)
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This article is cited in 1 scientific paper (total in 1 paper)
Limits of solutions to the singularly perturbed abstract hyperbolic-parabolic system
Andrei Perjan, Galina Rusu Department of Mathematics and Informatics, Moldova State University, A. Mateevici str. 60, MD 2009, Chisinau, Moldova
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 $\mathrm H$ as $\varepsilon\to0$, where $A(t)$, $t\in(0,\infty)$, is a family of linear self-adjoint operators.
Keywords and phrases:
singular perturbation, abstract second order Cauchy problem, boundary layer function, a priori estimate.
Received: 03.08.2014
Citation:
Andrei Perjan, Galina Rusu, “Limits of solutions to the singularly perturbed abstract hyperbolic-parabolic system”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2014, no. 3, 49–64
Linking options:
https://www.mathnet.ru/eng/basm371 https://www.mathnet.ru/eng/basm/y2014/i3/p49
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