Theory of a General Class of Dissipative Processes,
Abstract
The object of this paper is to develop a theory of periodic processes of sufficient generality that it can be applied to systems defined by partial differential equations (distributed parameter systems), functional differential equations of retarded and neutral type (hereditary systems), systems arising in the theory of elasticity, etc. The purpose here is to develop in the spirit of the work mentioned above a general and meaningful theory of dissipative periodic systems. More specifically the authors study the iterates of the period map T associated with a class of dissipative periodic processes, prove that large iterates of T always have fixed points, and characterize and prove the existence and stability of the maximal compact invarient set of T. Nonlinear ordinary differential equations which are periodic and dissipative were studied by Levinson in 1944. This paper also includes all of the results stated in a paper by LaSalle and Billotti. For ordinary differential equations, the period map T is topological and the space is locally compact. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1971
- Accession Number
- AD0717763
Entities
People
- J. K. Hale
- J. P. Lasalle
- Marshall Slemrod
Organizations
- Brown University