Accession Number : ADA292286

Title :   Discontinuous Solutions Of Semilinear Differential-Algebraic Equations Part I: Distribution Solutions.

Descriptive Note : Technical rept.,

Corporate Author : PITTSBURGH UNIV PA DEPT OF MATHEMATICS AND STATISTICS

Personal Author(s) : Rabier, Patrick J. ; Rheinboldt, Werner C.

PDF Url : ADA292286

Report Date : AUG 1994

Pagination or Media Count : 25

Abstract : There is strong physical evidence that a full treatment of differential-algebraic equations should be incorporate solutions with jump discontinuities. It is shown here that for semilinear problems the setting of distributions allows for the development of a theory where indeed such discontinuities may occur. This approach also settles the problem of inconsistent initial conditions in a very simple way. On the other hand, new issues arise as not only uniqueness. but even countability of the number of solutions of initial value problems may now be lost. A physically motivated but purely mathematical selection procedure to overcome this difficulty is discussed in part 2 of this paper. (AN)

Descriptors :   *DIFFERENTIAL EQUATIONS, *NONLINEAR ALGEBRAIC EQUATIONS, *LINEAR ALGEBRAIC EQUATIONS, SOLUTIONS(GENERAL), DISCONTINUITIES, SET THEORY, POINT THEOREM.

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE