Accession Number : AD0681829

Title :   CONTINUOUS TRANSFORMATIONS AND INTEGRAL MANIFOLDS.

Descriptive Note : Final rept. 1 Sep 65-31 Oct 68,

Corporate Author : MICHIGAN UNIV ANN ARBOR DEPT OF MATHEMATICS

Personal Author(s) : Cesari,Lamberto

Report Date : NOV 1968

Pagination or Media Count : 10

Abstract : During the reporting the principal investigator and some of his collaborators completed seventeen research papers. This work is described. The major effort was devoted to problems of optimal control. Existence theorems were proved for lumped parameter control systems by a new type of analysis. A number of related conditions were analyzed with examples and applications. Existence theorems were proved for distributed parameter control systems by the use of Sobolev spaces technique and for partial differential equations written in the rather general form proposed by Dieudonne and Rashevski. A form of Pontryagin's principle were proved for these systems which is remarkably similar to a K. A. Lurie problem of magnetohydrodynamic channel flow. Further work concerns: measure theory, integration over a surface area, periodic solutions of nonlinear hyperbolic partial differential equations, in particular, nonlinear wave equations. (Author)

Descriptors :   (*FUNCTIONAL ANALYSIS, *PARTIAL DIFFERENTIAL EQUATIONS), (*CONTROL SYSTEMS, OPTIMIZATION), TRANSFORMATIONS(MATHEMATICS), NONLINEAR DIFFERENTIAL EQUATIONS, CALCULUS OF VARIATIONS, VECTOR SPACES, MEASURE THEORY, NUMERICAL INTEGRATION, TOPOLOGY, PERIODIC VARIATIONS, MAGNETOHYDRODYNAMICS, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE