SINGULAR LIMITS OF SOLUTIONS TO THE CAUCHY PROBLEM FOR SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS IN HILBERT SPACES
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Abstract
We study the behavior of solutions to the problem(ε“u′′ε(t) +A1uε(t)”+
u′ε(t) +A0uε(t) =f(t), t >0,uε(0) =u0, u′ε(0) =u1,in the Hilbert space
H asε→0, whereA1andA0are two linear selfadjoint operators.
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RUSU, G. Singular limits of solutions to the Cauchy problem for second order linear differential equations in Hilbert spaces. In: Buletinul Academiei de Ştiinţe a Republicii Moldova : Matematica. 2009, nr. 3(61), pp. 81-95. ISSN 1024-76-96