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Math and StatisticsTheoretical Mathematics

Discontinuous Solutions Of Semilinear Differential-Algebraic Equations Part 2: Rho-Consistency

Authors: Patrick J. Rabier; Werner C. Rheinboldt; PITTSBURGH UNIV PA DEPT OF MATHEMATICS AND STATISTICS
Abstract:
Part 1 of this paper presented a theory of distribution solutions of semilinear differential-algebraic equations (DAE's). In particular, it was shown that uniqueness of solutions of initial value problems breaks down completely in the class of discontinuous solutions. Here a mathematical procedure is introduced for selecting physically acceptable solutions which satisfy some new consistency condition relative to admissible perturbations of the original DAE. Several nonlinear circuit examples are given to support the theory. (AN)

Limitations: APPROVED FOR PUBLIC RELEASE
Description: Technical rept.
Pages: 35
Report Date: AUG 94
Contract Number: N00014-90-J-1025, $NSF-CCR92-0
Report Number: A582292
Keywords relating to this report:
*DIFFERENTIAL EQUATIONS
*LINEAR ALGEBRAIC EQUATIONS
*NONLINEAR ALGEBRAIC EQUATIONS
APPROXIMATION_MATHEMATICS_
CAPACITORS
CIRCUIT ANALYSIS
CONSISTENCY
EIGENVALUES
INDUCTANCE
PARAMETERS
PERTURBATION THEORY
PERTURBATIONS
SOLUTIONS_GENERAL_
VECTOR ANALYSIS
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