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We consider mildly degenerate Kirchhoff equations with a small parameter anda weak dissipation term. We prove the existence of global solutions when theparameter is small with respect to the size of initial data. Then we provideglobal-in-time error estimates on the difference between the solution of ourproblem and the solution of the corresponding first order problem.

Hyperbolic-parabolic singular perturbation for mildly degenerate Kirchhoff equations with weak dissipation