Geodesic
Singularly perturbed Cauchy problem for abstract linear differential equations of second order in Hilbert spaces
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2008), pp. 195-204

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We study the behavior of solutions to the problem $$ \begin{cases} \varepsilon\bigl(u_\varepsilon''(t)+A_1u_\varepsilon(t)\bigr)+u_\varepsilon'(t)+A_0u_\varepsilon(t)=f(t), \quad t>0,\\ u_\varepsilon(0)=u_0, \quad u_\varepsilon'=u_1, \end{cases} $$ in the Hilbert space $H$ as $\varepsilon\mapsto 0$ where $A_1$ and $A_0$ are two linear selfadjoint operators. 
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     author = {A. Perjan and Galina Rusu},
     title = {Singularly perturbed {Cauchy} problem for abstract linear differential equations of second order in {Hilbert} spaces},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {195--204},
     publisher = {mathdoc},
     number = {1},
     year = {2008},
     language = {en},
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}
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A. Perjan; Galina Rusu. Singularly perturbed Cauchy problem for abstract linear differential equations of second order in Hilbert spaces. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2008), pp. 195-204. http://geodesic.mathdoc.fr/item/BASM_2008_1_a12/