Energy Decay of Solution to a Nonlinear Wave Equation of Kirchhoff Type

The paper studies the asymptotic behavior of solution to the initial boundary value problem for a nonlinear hyperbolic equation of Kirchhoff type utt-M(kA12uk2)Au+ut-|u|αu=0. It proves the global existence of solution by constructing a stable set and the energy exponential decay estimate by applying a lemma of V Komornik.