Czechoslovak Mathematical Journal, Vol. 48, No. 4, pp. 737-745, 1998

# Convergence estimate for second order Cauchy problems with a small parameter

## Branko Najman

Branko Najman, Department of Mathematics, University of Zagreb, 41000 Zagreb, Bijenicka 30, Croatia

Abstract: 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.

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