Persistence of Invariant Sets for Dissipative Evolution Equations Academic Article uri icon

abstract

  • 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 aC1inertial form, certain natural numerical approximations possess an inertial form close to that of the underlying PDE in theC1norm. © 1998 Academic Press.

author list (cited authors)

  • Jones, D. A., Stuart, A. M., & Titi, E. S.

citation count

  • 12

publication date

  • March 1998