Research articles

Singular limits of solutions to the Cauchy problem for second order linear differential equations in Hilbert spaces

Galina Rusu

Department of Mathematics and Informatics, Moldova State University, Cişinău, Moldova

Abstract: 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.

Keywords and phrases: singular perturbations, Cauchy problem, boundary function.

MSC: 35B25, 35K15, 35L15, 34G10

Received: 15.07.2009

Language: English

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