Smoothness of Bounded Solutions of Nonlinear Evolution Equations.
Abstract
It is shown, that in many cases globally defined, bounded solutions of evolution equations are as smooth (in time) as the corresponding operator, even if a general solution of the initial value problem is much less smooth; i.e., initial values for bounded solutions are selected in such a way that optimal smoothness is attained. In particular, solutions which bifurcate from certain steady states such as periodic orbits, almost-periodic orbits and also homo- and heteroclinic orbits have this property. As examples a neutral functional differential equation, a slightly damped non-linear wave equation, and a heat equation are considered. In the latter case the space variable is included into the discussion of smoothness. Finally, generalized Hopf bifurcation in infinite dimensions is considered. Here this document discusses smoothness of the bifurcation function and generalize known results on the order of a focus. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 20, 1983
- Accession Number
- ADA135294
Entities
People
- J. K. Hale
- J. Scheurle
Organizations
- Brown University