## Differential and Integral Equations

### Global solvability and decay of the energy for the nonhomogeneous Kirchhoff equation

#### Abstract

We study the existence, uniqueness and stability of global strong solutions to the mixed problem for the nonhomogeneous Kirchhoff equation $$u_{tt}(x,t) - \varphi (x,t) M \Big (\int_{\Omega} \mid \nabla u(\xi,t) \mid^{2}\, d\xi \Big ) \Delta u(x,t) + g(x, t, u_{t}(x,t)) = 0$$ with small initial data.

#### Article information

Source
Differential Integral Equations, Volume 15, Number 10 (2002), 1219-1236.

Dates
First available in Project Euclid: 21 December 2012