Rigorous numerics for stationary solutions of dissipative PDEs - Existence and local dynamics -

Abstract

We show a criterion for verifying the locally unique existence of stationary solutions of a class of partial differential equations and the local dynamics around them with computer assistance. Our method is designed so that, in near future, it can be extended to further analysis of dynamics, like connecting orbits between equilibria. Several sample examples for verifying hyperbolic equilibria of a concrete PDE are also shown.