Green’s Function of the Cauchy Problem for Equations with Dissipative Parabolicity, Negative Genus, and Variable Coefficients
Green’s function of the Cauchy problem is constructed by the method of successive approximations, and its main properties are studied for a new class of linear differential equations with dissipative parabolicity and negative genus, whose coefficients are bounded, continuous in time, and infinitely...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2024/7137300 |
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| _version_ | 1832543785325690880 |
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| author | Vladyslav Litovchenko Denys Kharyna |
| author_facet | Vladyslav Litovchenko Denys Kharyna |
| author_sort | Vladyslav Litovchenko |
| collection | DOAJ |
| description | Green’s function of the Cauchy problem is constructed by the method of successive approximations, and its main properties are studied for a new class of linear differential equations with dissipative parabolicity and negative genus, whose coefficients are bounded, continuous in time, and infinitely differentiable by the spatial variable of the function. This class covers Shilov parabolic equations, as well as the class of the Zhitomirskii parabolic Shilov-type equations with variable coefficients and negative genus, and successfully complements the Petrovsky class of parabolic equations. |
| format | Article |
| id | doaj-art-8e3f44d1a89248a384c5bf9bed5b1bc3 |
| institution | Kabale University |
| issn | 1687-9651 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-8e3f44d1a89248a384c5bf9bed5b1bc32025-02-03T11:30:42ZengWileyInternational Journal of Differential Equations1687-96512024-01-01202410.1155/2024/7137300Green’s Function of the Cauchy Problem for Equations with Dissipative Parabolicity, Negative Genus, and Variable CoefficientsVladyslav Litovchenko0Denys Kharyna1Chernivtsi National UniversityChernivtsi National UniversityGreen’s function of the Cauchy problem is constructed by the method of successive approximations, and its main properties are studied for a new class of linear differential equations with dissipative parabolicity and negative genus, whose coefficients are bounded, continuous in time, and infinitely differentiable by the spatial variable of the function. This class covers Shilov parabolic equations, as well as the class of the Zhitomirskii parabolic Shilov-type equations with variable coefficients and negative genus, and successfully complements the Petrovsky class of parabolic equations.http://dx.doi.org/10.1155/2024/7137300 |
| spellingShingle | Vladyslav Litovchenko Denys Kharyna Green’s Function of the Cauchy Problem for Equations with Dissipative Parabolicity, Negative Genus, and Variable Coefficients International Journal of Differential Equations |
| title | Green’s Function of the Cauchy Problem for Equations with Dissipative Parabolicity, Negative Genus, and Variable Coefficients |
| title_full | Green’s Function of the Cauchy Problem for Equations with Dissipative Parabolicity, Negative Genus, and Variable Coefficients |
| title_fullStr | Green’s Function of the Cauchy Problem for Equations with Dissipative Parabolicity, Negative Genus, and Variable Coefficients |
| title_full_unstemmed | Green’s Function of the Cauchy Problem for Equations with Dissipative Parabolicity, Negative Genus, and Variable Coefficients |
| title_short | Green’s Function of the Cauchy Problem for Equations with Dissipative Parabolicity, Negative Genus, and Variable Coefficients |
| title_sort | green s function of the cauchy problem for equations with dissipative parabolicity negative genus and variable coefficients |
| url | http://dx.doi.org/10.1155/2024/7137300 |
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