Existence, uniqueness and exponential decay of solutions to kirchhoff equation in ℝn

Abstract

We discuss the global well-posedness and uniform exponential stability for the Kirchhoff equation in ℝn (Formula presented) The global solvability is proved when the initial data are taken small enough and the exponential decay of the energy is obtained in the strong topology H2(ℝn) × H1(ℝn), which is a different feature of the present article when compared with the prior literature. We also dedicate a section to discuss a model with the frictional damping term λut, is replaced by a viscoelastic damping term ∫t 0 g(t-s)Δu(s)ds.