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Overdetermined Elliptic Systems

Foundations of Computational Mathematics, 2005
We consider linear overdetermined systems of partial differential equations. We show that the introduction of weights classically used for the definition of ellipticity is not necessary, as any system that is elliptic with respect to some weights becomes elliptic without weights during its completion to involution.
Werner M Seiler   +2 more
exaly   +2 more sources

GIC Modelling for an Overdetermined System

2006 Canadian Conference on Electrical and Computer Engineering, 2006
Geomagnetically induced currents in power systems can cause problems ranging from overload of transformers to power blackout. Modelling can be used to show the GIC flow throughout a power system; however, the modelled GIC values have uncertainties because of the simplifying assumptions.
Alexandre A. Trichtchenko   +2 more
openaire   +1 more source

An overdetermined system

Quarterly of Applied Mathematics, 1983
The Korteweg stress tensor has been the object of considerable interest recently since it provides a purely mechanical approach to the problem of liquid-vapor phase equilibria independent of various thermodynamical assumptions. Here we show that, unless rather special conditions are satisfied, the only physical phase boundaries which are consistent ...
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Overdetermined and Underdetermined Systems

2018
As we know, overdetermined systems have no solution while underdetermined systems have infinitely many solutions.
Joseph L. Awange   +3 more
openaire   +1 more source

Lateral overdetermination of the FitzHugh–Nagumo system

Inverse Problems, 2004
Summary: The FitzHugh-Nagumo system, composed of a semilinear parabolic equation coupled to a linear ordinary equation \[ v_t=v_{xx}+f(v)-w, \quad ...
Cox, Steven, Wagner, Alfred
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Overdetermined Systems of Linear Equations

SIAM Review, 1963
for all x we call a Cebysev (approximate) solution (for short, C.S.) of (1).3 This report is a study of the properties of Cebysev solutions of (1). Most of the results we shall obtain may be found, explicitly or implicitly, in the literature. In particular this exposition relies on the presentations of Rivlin and Shapiro [1] and of Rademacher and ...
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Solutions of Overdetermined Systems

2016
In geodesy and geoinformatics, field observations are normally collected with the aim of estimating parameters. Very frequently, one has to handle overdetermined systems of nonlinear equations. In such cases, there exist more equations than unknowns, therefore “the solution” of the system can be interpreted only in a certain error metric, i.e., least ...
Joseph L. Awange, Béla Paláncz
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