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

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 $x\to \infty$.