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 ...

In this paper, we prove the exponential decay as time goes to infinity of regular solutions of the problem for the Kirchhoff wave equation with nonlocal condition and weak dampingu(tt) - M (\\delU\\(2)(2)) Deltau + ...

In this paper, we prove the exponential decay as time goes to infinity of regular solutions of the problem for the Kirchhoff wave equation with nonlocal condition and weak dampingu(tt) - M (\\delU\\(2)(2)) Deltau + ...

This paper is concerned with a viscoelastic Kirchhoff plate featuring variable material density. It is modeled by the equation (Formula presented.) defined in a bounded domain of R N , where ϱ = |u t | ρ accounts for a ...

We discuss the global well-posedness and uniform exponential stability for the Kirchhoff equation in R-n u(tt) - M(integral(Rn) vertical bar Delta u vertical bar(2)dx)Delta u + lambda(ut) = 0 in R-n x (0, infinity). The ...

We shall discuss a characterization of resonances in terms of the asymptotic decay of solutions. One expect that this decay should occur in an almost exponential fashion. We prove this fact in the shape resonance model. We ...