## Differential and Integral Equations

### On internal elastic membrane with strong damping

#### Abstract

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

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

Dates
First available in Project Euclid: 27 December 2012

https://projecteuclid.org/euclid.die/1356628825

Mathematical Reviews number (MathSciNet)
MR2830311

Zentralblatt MATH identifier
1249.35217

#### Citation

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