Geodesic
Steady-state solutions in an algebra of generalized functions
Novi Sad Journal of Mathematics, Tome 45 (2015) no. 1.

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Formulas for the solutions of initial value problems for ordinary differential equations with singular $\delta^{(n)}$-like driving terms are derived in the framework of an algebra of generalized functions (of Colombeau type) over a field of generalized scalars. Some of the solutions might have physical meaning - such as of the electrical current after lightning or under superconductivity - but do not have counterparts in the theory of Schwartz distributions. What is somewhat unusual (compared with other similar works) is the involvement of infinitely large constants, such as $\delta(0)$, in some of the formulas for the solutions.
Publié le :
DOI : 10.30755/NSJOM.GF14.06
Classification : 46F30, 44A10, 46F10, 46S30, 46S20, 34A12, 34E18, 34A37, 35A08
Keywords: Ordinary differential equation with constant coefficients, Steady-state solution, distributional solution, generalized solution, Colombeau algebra of generalized functions, Schwartz distributions, Green function, infinitesimal number, finite number, infinitely large number, Kirchoff law, LRC-electrical circuit, lightning, lightning rod, superconductivity 
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Todor D. Todorov. Steady-state solutions in an algebra of generalized functions. Novi Sad Journal of Mathematics, Tome 45 (2015) no. 1. doi : 10.30755/NSJOM.GF14.06. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.GF14.06/

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