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2006 Time behavior for a class of nonlinear beam equations
C. Buriol, G. Perla Menzala
Differential Integral Equations 19(1): 15-29 (2006).

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 $1 \le n \le 5$.

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C. Buriol. G. Perla Menzala. "Time behavior for a class of nonlinear beam equations." Differential Integral Equations 19 (1) 15 - 29, 2006.

Information

Published: 2006
First available in Project Euclid: 21 December 2012

zbMATH: 1212.35476
MathSciNet: MR2192760

Subjects:
Primary: 35Q72
Secondary: 35B40 , 35L75 , 74H40 , 74K10

Rights: Copyright © 2006 Khayyam Publishing, Inc.

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Vol.19 • No. 1 • 2006
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