Persistence of Invariant Sets for Dissipative Evolution Equations

We show that results concerning the persistence of invariant sets of ordinary differential equations under perturbation may be applied directly to a certain class of partial differential equations. Our framework is particularly well-suited to encompass numerical approximations of these partial differential equations. Specifically, we show that for a class of PDEs with a C1 inertial form, certain natural numerical approximations possess an inertial form close to that of the underlying PDE in the C1 norm.