Genericity of the Morse-Smale Property for Damped Wave Equations

We prove that for damped hyperbolic equations the Morse-Smale property (hyperbolicity of equilibria and transversal intersection of stable and unstable manifolds) is generic. More precisely, we prove that in an appropriate functional space of nonlinear terms in the equation, the set of functions for which the latter has the Morse-Smale property is residual, i.e., it is a countable intersection of open dense sets. The result extends a similar result proved in 1] for reaction diffusion equations. However, because of the absence of knowledge about nodal sets of polutions new ideas were needed in the proof.