Invariant manifolds of partial functional differential equations.
The authors give a proof for the existence and attractivity of center-unstable, center and stable manifolds for general evolutionary processes using the method of graph transforms. They indicate that their results can be applied to a large class of equations generating evolutionary processes that may not be strongly continuous. They then use some classical results on smoothness of invariant manifolds for maps and the technique of ``lifting'' to obtain the smoothness of invariant manifolds. The smoothness result requires the nonlinear perturbation to be \(C^k\)-smooth.
partial functional-differential equation
scientific article; zbMATH DE number 2062885
scientific article