Global existence and uniform decay rates for the Kirchhoff-Carrier equation with nonlinear dissipation

This paper is devoted to the existence of global solutions of the Kirchhoff-Carrier equation uₜₜ-M(t,∫Ω|∇ u|²dx)Δ u=0 subject to nonlinear boundary dissipation. Assuming that M(t,λ )≥ m₀>0, we prove the existence and uniqueness of regular solutions without any smallness on the initial data. Moreover, uniform decay rates are obtained by assuming a nonlinear feedback acting on the boundary.