Hyperbolic–parabolic singular perturbation for quasilinear equations of Kirchhoff type

We consider a hyperbolic–parabolic singular perturbation problem for a quasilinear equation of Kirchhoff type, and obtain parameter-dependent time decay estimates of the difference between the solutions of a quasilinear dissipative hyperbolic equation of Kirchhoff type and the corresponding quasilinear parabolic equation. For this purpose we show time decay estimates for hyperbolic–parabolic singular perturbation problem for linear equations with a time-dependent coefficient.