Differential and Integral Equations

On internal elastic membrane with strong damping

F.D. Araruna, M.R. Clark, and O.A. Lima

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In this work we study existence and uniqueness of solutions to the abstract framework related to the Kirchhoff model for small deformations of a membrane \[ u'' +M ( \| u \| ^{2} ) Au+ F(u)+Au'=0, \] when $M$ is degenerate and $A,$ $F$ are operators. Furthermore, we obtain the asymptotic behavior, as $t \rightarrow\infty,$ of solutions in a concrete case.

Article information

Differential Integral Equations, Volume 24, Number 7/8 (2011), 601-618.

First available in Project Euclid: 27 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35L70: Nonlinear second-order hyperbolic equations 74G25: Global existence of solutions 35B40: Asymptotic behavior of solutions


Araruna, F.D.; Clark, M.R.; Lima, O.A. On internal elastic membrane with strong damping. Differential Integral Equations 24 (2011), no. 7/8, 601--618. https://projecteuclid.org/euclid.die/1356628825

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