THE STABILITY OF ROLL SOLUTIONS OF THE 2-DIMENSIONAL SWIFT-HOHENBERG EQUATION AND THE PHASE-DIFFUSION EQUATION

A stability criterion of roll solutions of the two-dimensional Swift-H ohenberg equation is presented. It clarifies the effect of the system size on the primary instabilty of rolls. An interpretation of the phas e-diffusion equation is also given from the viewpoint of spectral anal ysis. The key to carrying out the spectral analysis is that the infini te-dimensional system of linear equations naturally induced by the Fou rier decomposition for the linearized eigenvalue problem of the roll s olution can be reduced to the three-dimensional system.