Advances in Differential Equations

Global existence and uniform decay rates for the Kirchhoff-Carrier equation with nonlinear dissipation

M. M. Cavalcanti, V. N. Domingos Cavalcanti, and J. A. Soriano

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Abstract

This paper is devoted to the existence of global solutions of the \newline Kirchhoff-Carrier equation $$u_{tt}-M\bigl(t,\int_{\Omega}\left|\nabla u\right|^2dx\bigr)\Delta u=0$$ subject to nonlinear boundary dissipation. Assuming that $M(t,\lambda )\geq m_0>0$, we prove the existence and uniqueness of regular solutions without any smallness on the initial data. Moreover, uniform decay rates are obtained by assuming a nonlinear feedback acting on the boundary.

Article information

Source
Adv. Differential Equations Volume 6, Number 6 (2001), 701-730.

Dates
First available in Project Euclid: 2 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1357140586

Mathematical Reviews number (MathSciNet)
MR1829093

Zentralblatt MATH identifier
1007.35049

Subjects
Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 35B40: Asymptotic behavior of solutions 35L05: Wave equation 35L35: Initial-boundary value problems for higher-order hyperbolic equations

Citation

Cavalcanti, M. M.; Domingos Cavalcanti, V. N.; Soriano, J. A. Global existence and uniform decay rates for the Kirchhoff-Carrier equation with nonlinear dissipation. Adv. Differential Equations 6 (2001), no. 6, 701--730. https://projecteuclid.org/euclid.ade/1357140586.


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