Construction of the fundamental solution of a class of degenerate parabolic equations of high order
In the article, using the modified Levy method, a Green's function for a class of ultraparabolic equations of high order with an arbitrary number of parabolic degeneration groups is constructed. The modified Levy method is developed for high-order Kolmogorov equations with coefficients dependin...
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2020-06-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
| Subjects: | |
| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/3871 |
| _version_ | 1797205874309070848 |
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| author | H.P. Malytska I.V. Burtnyak |
| author_facet | H.P. Malytska I.V. Burtnyak |
| author_sort | H.P. Malytska |
| collection | DOAJ |
| description | In the article, using the modified Levy method, a Green's function for a class of ultraparabolic equations of high order with an arbitrary number of parabolic degeneration groups is constructed. The modified Levy method is developed for high-order Kolmogorov equations with coefficients depending on all variables, while the frozen point, which is a parametrix, is chosen so that an exponential estimate of the fundamental solution and its derivatives is conveniently used. |
| first_indexed | 2024-04-24T08:58:03Z |
| format | Article |
| id | doaj.art-e12e6da7c13743f7b588bf3d131593a7 |
| institution | Directory Open Access Journal |
| issn | 2075-9827 2313-0210 |
| language | English |
| last_indexed | 2024-04-24T08:58:03Z |
| publishDate | 2020-06-01 |
| publisher | Vasyl Stefanyk Precarpathian National University |
| record_format | Article |
| series | Karpatsʹkì Matematičnì Publìkacìï |
| spelling | doaj.art-e12e6da7c13743f7b588bf3d131593a72024-04-16T07:00:37ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102020-06-01121798710.15330/cmp.12.1.79-873365Construction of the fundamental solution of a class of degenerate parabolic equations of high orderH.P. Malytska0I.V. Burtnyak1https://orcid.org/0000-0002-9440-1467Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, UkraineVasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, UkraineIn the article, using the modified Levy method, a Green's function for a class of ultraparabolic equations of high order with an arbitrary number of parabolic degeneration groups is constructed. The modified Levy method is developed for high-order Kolmogorov equations with coefficients depending on all variables, while the frozen point, which is a parametrix, is chosen so that an exponential estimate of the fundamental solution and its derivatives is conveniently used.https://journals.pnu.edu.ua/index.php/cmp/article/view/3871degenerated parabolic equationsmodified levy's methodkolmogorov's equationfundamental solutionparametrix |
| spellingShingle | H.P. Malytska I.V. Burtnyak Construction of the fundamental solution of a class of degenerate parabolic equations of high order Karpatsʹkì Matematičnì Publìkacìï degenerated parabolic equations modified levy's method kolmogorov's equation fundamental solution parametrix |
| title | Construction of the fundamental solution of a class of degenerate parabolic equations of high order |
| title_full | Construction of the fundamental solution of a class of degenerate parabolic equations of high order |
| title_fullStr | Construction of the fundamental solution of a class of degenerate parabolic equations of high order |
| title_full_unstemmed | Construction of the fundamental solution of a class of degenerate parabolic equations of high order |
| title_short | Construction of the fundamental solution of a class of degenerate parabolic equations of high order |
| title_sort | construction of the fundamental solution of a class of degenerate parabolic equations of high order |
| topic | degenerated parabolic equations modified levy's method kolmogorov's equation fundamental solution parametrix |
| url | https://journals.pnu.edu.ua/index.php/cmp/article/view/3871 |
| work_keys_str_mv | AT hpmalytska constructionofthefundamentalsolutionofaclassofdegenerateparabolicequationsofhighorder AT ivburtnyak constructionofthefundamentalsolutionofaclassofdegenerateparabolicequationsofhighorder |