Differential and Integral Equations

Time behavior for a class of nonlinear beam equations

C. Buriol and G. Perla Menzala

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Abstract

We consider a class of nonlinear beam equations in the whole space $\mathbb R^n$. Using previous important work due to Levandovsky and Strauss we prove that, locally, the $H^1$-norm of a strong solution approaches zero as $t \to +\infty$ as long as the spatial dimension $n \ge 6$. The problem remains open for dimensions $1 \le n \le 5$.

Article information

Source
Differential Integral Equations, Volume 19, Number 1 (2006), 15-29.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356050530

Mathematical Reviews number (MathSciNet)
MR2192760

Zentralblatt MATH identifier
1212.35476

Subjects
Primary: 35Q72
Secondary: 35B40: Asymptotic behavior of solutions 35L75: Nonlinear higher-order hyperbolic equations 74H40: Long-time behavior of solutions 74K10: Rods (beams, columns, shafts, arches, rings, etc.)

Citation

Buriol, C.; Perla Menzala, G. Time behavior for a class of nonlinear beam equations. Differential Integral Equations 19 (2006), no. 1, 15--29. https://projecteuclid.org/euclid.die/1356050530


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