Accession Number : AD0618851

Title :   A STABILITY THEORY FOR NONLINEAR MIXED INITIAL BOUNDARY VALUE PROBLEMS,

Corporate Author : IBM WATSON RESEARCH CENTER YORKTOWN HEIGHTS N Y

Personal Author(s) : Brayton,R. K. ; Miranker,W. L.

Report Date : 19 JUN 1964

Pagination or Media Count : 20

Abstract : This paper discusses the notion of complete stability of mixed initial boundary problems for systems of partial differential equations. The discussion is not restricted to the purely linear case. Moreover, the boundary conditions are permitted to take the form of systems of nonlinear ordinary differential equations. The principal result of the paper is a method for constructing so-called Liapounov functionals by means of which the stability statement is obtained. A second result is a theorem which shows that complete stability follows from the existence of a Liapounov functional. A number of examples are included.

Descriptors :   (*STABILITY, THEOREMS), (*BOUNDARY VALUE PROBLEMS, THEORY), (*NONLINEAR DIFFERENTIAL EQUATIONS, BOUNDARY VALUE PROBLEMS), FUNCTIONAL ANALYSIS

Distribution Statement : APPROVED FOR PUBLIC RELEASE