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

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  • Zhenbang Li
  • Changchun Liu

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 ð » 4 perturbations. These traveling wave solutions converge to a constant as ð ‘¥ → ∞ .

Suggested Citation

  • Zhenbang Li & Changchun Liu, 2012. "On the Nonlinear Instability of Traveling Waves for a Sixth-Order Parabolic Equation," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-17, September.
    • Handle: RePEc:hin:jnlaaa:739156
    DOI: 10.1155/2012/739156
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    Cited by:

    1. José Luis Díaz Palencia & Julián Roa González & Almudena Sánchez Sánchez, 2022. "Study of Solutions for a Degenerate Reaction Equation with a High Order Operator and Advection," Mathematics, MDPI, vol. 10(10), pages 1-18, May.

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