Attractor bifurcation and final patterns of the \(N\)-dimensional and generalized Swift-Hohenberg equations (Q2469390)

The author investigates the bifurcation of the Swift-Hohenberg equation and the generalized Swift-Hohenberg equation with Dirichlet boundary conditions. His work relies on a variant of bifurcation theory by Ma and Wang, which is shortly presented in the second section. In the following section the critical eigenvalues and corresponding eigenfunctions of the Swift-Hohenberg equation and the generalized Swift-Hohenberg equation in one and \(n\) space dimensions and the corresponding center manifold equations are given. Also the structure of the bifurcating equations is indicated.