Gradient Structures Associated with a Polynomial Differential Equation
In this paper, by using the characteristic system method, the kernel of a polynomial differential equation involving a derivation in <inline-formula> <math display="inline"> <semantics> <mstyle displaystyle="true" scriptlevel="0"> <msup> &l...
| मुख्य लेखक: | |
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| स्वरूप: | लेख |
| भाषा: | English |
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MDPI AG
2020-04-01
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| श्रृंखला: | Mathematics |
| विषय: | |
| ऑनलाइन पहुंच: | https://www.mdpi.com/2227-7390/8/4/535 |
| _version_ | 1827719281710727168 |
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| author | Savin Treanţă |
| author_facet | Savin Treanţă |
| author_sort | Savin Treanţă |
| collection | DOAJ |
| description | In this paper, by using the characteristic system method, the kernel of a polynomial differential equation involving a derivation in <inline-formula> <math display="inline"> <semantics> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>R</mi> <mi>n</mi> </msup> </mstyle> </semantics> </math> </inline-formula> 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. |
| first_indexed | 2024-03-10T20:40:08Z |
| format | Article |
| id | doaj.art-79c365ff7a3a43e29b7059a06b3e92c4 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T20:40:08Z |
| publishDate | 2020-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-79c365ff7a3a43e29b7059a06b3e92c42023-11-19T20:44:03ZengMDPI AGMathematics2227-73902020-04-018453510.3390/math8040535Gradient Structures Associated with a Polynomial Differential EquationSavin Treanţă0Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, RomaniaIn this paper, by using the characteristic system method, the kernel of a polynomial differential equation involving a derivation in <inline-formula> <math display="inline"> <semantics> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>R</mi> <mi>n</mi> </msup> </mstyle> </semantics> </math> </inline-formula> 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.https://www.mdpi.com/2227-7390/8/4/535scalar derivationLie algebragradient systempolynomial differential equationflowkernel |
| spellingShingle | Savin Treanţă Gradient Structures Associated with a Polynomial Differential Equation Mathematics scalar derivation Lie algebra gradient system polynomial differential equation flow kernel |
| title | Gradient Structures Associated with a Polynomial Differential Equation |
| title_full | Gradient Structures Associated with a Polynomial Differential Equation |
| title_fullStr | Gradient Structures Associated with a Polynomial Differential Equation |
| title_full_unstemmed | Gradient Structures Associated with a Polynomial Differential Equation |
| title_short | Gradient Structures Associated with a Polynomial Differential Equation |
| title_sort | gradient structures associated with a polynomial differential equation |
| topic | scalar derivation Lie algebra gradient system polynomial differential equation flow kernel |
| url | https://www.mdpi.com/2227-7390/8/4/535 |
| work_keys_str_mv | AT savintreanta gradientstructuresassociatedwithapolynomialdifferentialequation |