Convergence estimate for second order Cauchy problems with a small parameter
Czechoslovak Mathematical Journal, Tome 48 (1998) no. 4, pp. 737-745.

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We consider the second order initial value problem in a Hilbert space, which is a singular perturbation of a first order initial value problem. The difference of the solution and its singular limit is estimated in terms of the small parameter $\varepsilon .$ The coefficients are commuting self-adjoint operators and the estimates hold also for the semilinear problem.
Classification : 34E15, 34G20, 35B25, 35R15, 47N20 
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     author = {Najman, Branko},
     title = {Convergence estimate for second order {Cauchy} problems with a small parameter},
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     pages = {737--745},
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     volume = {48},
     number = {4},
     year = {1998},
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     zbl = {0952.35151},
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Najman, Branko. Convergence estimate for second order Cauchy problems with a small parameter. Czechoslovak Mathematical Journal, Tome 48 (1998) no. 4, pp. 737-745. https://geodesic-test.mathdoc.fr/item/CMJ_1998__48_4_a10/