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Open AccessArticle

Gradient Structures Associated with a Polynomial Differential Equation

Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania
Mathematics 2020, 8(4), 535; https://doi.org/10.3390/math8040535
Received: 19 March 2020 / Revised: 31 March 2020 / Accepted: 31 March 2020 / Published: 4 April 2020
In this paper, by using the characteristic system method, the kernel of a polynomial differential equation involving a derivation in R n is described by solving the Cauchy Problem for the corresponding first order system of PDEs. Moreover, the kernel representation has a special significance on the space of solutions to the corresponding system of PDEs. As very important applications, it has been established that the mathematical framework developed in this work can be used for the study of some second-order PDEs involving a finite set of derivations. View Full-Text
Keywords: scalar derivation; Lie algebra; gradient system; polynomial differential equation; flow; kernel scalar derivation; Lie algebra; gradient system; polynomial differential equation; flow; kernel
MDPI and ACS Style

Treanţă, S. Gradient Structures Associated with a Polynomial Differential Equation. Mathematics 2020, 8, 535.

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