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

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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

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060752

Mathematical Reviews number (MathSciNet)
MR1919769

Zentralblatt MATH identifier
1011.35097

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

Citation

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


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