Differential and Integral Equations

Rates of decay of a nonlocal beam equation

H. Lange and G. Perla Menzala

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Abstract

We consider a beam equation with a nonlocal nonlinearity of Kirchhoff type on an unbounded domain. We show that smooth global solutions decay (in time) at a uniform rate as $t\to +\infty$. Our model is closely related to a nonlinear Schrödinger equation with a time-dependent dissipation. We use this observation to obtain intermediate information on our original model.

Article information

Source
Differential Integral Equations, Volume 10, Number 6 (1997), 1075-1092.

Dates
First available in Project Euclid: 1 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367438220

Mathematical Reviews number (MathSciNet)
MR1608033

Zentralblatt MATH identifier
0940.35191

Subjects
Primary: 35Q72
Secondary: 35B40: Asymptotic behavior of solutions 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]

Citation

Lange, H.; Perla Menzala, G. Rates of decay of a nonlocal beam equation. Differential Integral Equations 10 (1997), no. 6, 1075--1092. https://projecteuclid.org/euclid.die/1367438220


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