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