2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/214099We consider the hyperbolic-parabolic singular perturbation problem for a nondegenerate quasilinear equation of Kirchhoff type with weak dissipation. This means that the dissipative term is multiplied by a coefficient b(t) which tends to 0 as t tends to +infinity. The case where b(t) behaves like (1+t)^{-p} with p<1 has recently been considered. The result is that the hyperbolic problem has a unique global solution, and the difference between solutions of the hyperbolic problem and the corresponding solutions of the parabolic problem converges to zero both as t tends to +infinity and as epsilon goes to 0. In this paper we show that these results cannot be true for p>1, but they remain true in the critical case p=1.22 pagesAnalysis of PDEs35B25; 35B40; 35L70.text