Accession Number : AD0717763

Title :   Theory of a General Class of Dissipative Processes,

Corporate Author : BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS

Personal Author(s) : Hale,J. K. ; LaSalle,J. P. ; Slemrod,Marshall

Report Date : JAN 1971

Pagination or Media Count : 27

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)

Descriptors :   (*FUNCTIONAL ANALYSIS, *DIFFERENTIAL EQUATIONS), CONTROL SYSTEMS, ELASTIC PROPERTIES, NONLINEAR DIFFERENTIAL EQUATIONS, BANACH SPACE, SET THEORY, TOPOLOGY, PERIODIC VARIATIONS, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE