Abstract and Applied Analysis
Volume 2012 (2012), Article ID 739156, 17 pages
http://dx.doi.org/10.1155/2012/739156
Research Article

On the Nonlinear Instability of Traveling Waves for a Sixth-Order Parabolic Equation

Zhenbang Li and Changchun Liu

Department of Mathematics, Jilin University, Changchun 130012, China

Received 4 June 2012; Accepted 2 August 2012

Academic Editor: Ljubisa Kocinac

Copyright © 2012 Zhenbang Li and Changchun Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the instability of the traveling waves of a sixth-order parabolic equation which arises naturally as a continuum model for the formation of quantum dots and their faceting. We prove that some traveling wave solutions are nonlinear unstable under 𝐻 4 perturbations. These traveling wave solutions converge to a constant as 𝑥 → ∞ .