Differential and Integral Equations

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

Alfredo T. Cousin, Cícero L. Frota, and Nickolai A. Lar'kin

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 35B35: Stability 35B40: Asymptotic behavior of solutions


Cousin, Alfredo T.; Frota, Cícero L.; Lar'kin, Nickolai A. Global solvability and decay of the energy for the nonhomogeneous Kirchhoff equation. Differential Integral Equations 15 (2002), no. 10, 1219--1236. https://projecteuclid.org/euclid.die/1356060752

Export citation