
Accession Number : ADA292286
Title : Discontinuous Solutions Of Semilinear DifferentialAlgebraic 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 differentialalgebraic 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