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

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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. 
@article{BASM_2009_3_a8,
     author = {Galina Rusu},
     title = {Singular limits of solutions to the {Cauchy} problem for second order linear differential equations in {Hilbert} spaces},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {81--95},
     publisher = {mathdoc},
     number = {3},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2009_3_a8/}
}
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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/