Geodesic
Singular limits of solutions to the Cauchy problem for second order linear differential equations in Hilbert spaces
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2009), pp. 81-95 
Galina Rusu. Singular limits of solutions to the Cauchy problem for second order linear differential equations in Hilbert spaces. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2009), pp. 81-95. http://geodesic.mathdoc.fr/item/BASM_2009_3_a8/
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     title = {Singular limits of solutions to the {Cauchy} problem for second order linear differential equations in {Hilbert} spaces},
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     url = {http://geodesic.mathdoc.fr/item/BASM_2009_3_a8/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We study the behavior of solutions to the problem $$ \begin{cases} \varepsilon\Big(u''_\varepsilon(t)+A_1u_\varepsilon(t)\Big)+u'_\varepsilon(t)+ A_0u_\varepsilon(t)=f(t),\quad t>0,\\ u_\varepsilon(0)=u_0,\qquad u'_\varepsilon(0)=u_1, \end{cases} $$ in the Hilbert space $H$ as $\varepsilon\to0$, where $A_1$ and $A_0$ are two linear selfadjoint operators.

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