The Phase Space of an Initial-Boundary Value Problem for the Hoff Equation

The Hoff equation $(\lambda +\Delta )u_t=-\alpha u-\beta u^3$ describes the H-beam buckling dynamics. We show that the phase space of the Hoff equation is a simple $C^\infty $ Banach manifold modeled on a subspace complementary to the kernel $\ker (\lambda +\Delta )$.