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2001 Global existence and uniform decay rates for the Kirchhoff-Carrier equation with nonlinear dissipation
M. M. Cavalcanti, V. N. Domingos Cavalcanti, J. A. Soriano
Adv. Differential Equations 6(6): 701-730 (2001).

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.

Citation

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M. M. Cavalcanti. V. N. Domingos Cavalcanti. J. A. Soriano. "Global existence and uniform decay rates for the Kirchhoff-Carrier equation with nonlinear dissipation." Adv. Differential Equations 6 (6) 701 - 730, 2001.

Information

Published: 2001
First available in Project Euclid: 2 January 2013

zbMATH: 1007.35049
MathSciNet: MR1829093

Subjects:
Primary: 35L70
Secondary: 35B40, 35L05, 35L35

Rights: Copyright © 2001 Khayyam Publishing, Inc.

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Vol.6 • No. 6 • 2001
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