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

摘要

The paper studies the asymptotic behavior of solution to the initial boundary value problem for a nonlinear hyperbolic equation of Kirchhoff type utt.M(∥A 1 2 u∥2)Au + ut.|u|u = 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.