Exponential decay for the solutions of wave equations of Kirchhoff type with strong damping (Q1603247)

The authors study some decay estimates of the energy of the nonlinear problem of Kirchhoff type: \[ y''(t)-M(|\nabla y(t)|^2)\Delta y(t)-\delta\Delta y'(y)=f(t) \] with some \(C^1(0,\infty)\) function \(M\) and with the damping constant \(\delta>0\), in a bounded domain. Undamped mixed boundary conditions are considered. The main result indicates an exponential decay of the energy when \(t\to \infty\).