Fundamental Solution for a New Class of Non-Archimedean Pseudo-Differential Equations
In this paper we study a new class of pseudo-differential equations on functions of two $p$-adic variables. It is proved that the correspondent Cauchy problem has a unique solution. Some properties of this solution are studied, in particular, the finite dependence property and an $L^1$-estimate.
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| Format: | Article |
| Language: | English |
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Odesa National University of Technology
2025-06-01
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| Series: | Pracì Mìžnarodnogo Geometričnogo Centru |
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| Online Access: | https://journals.ontu.edu.ua/index.php/geometry/article/view/2849 |
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| author | Марія Вікторівна Сердюк Анатолій Наумович Кочубей |
| author_facet | Марія Вікторівна Сердюк Анатолій Наумович Кочубей |
| author_sort | Марія Вікторівна Сердюк |
| collection | DOAJ |
| description | In this paper we study a new class of pseudo-differential equations on functions of two $p$-adic variables. It is proved that the correspondent Cauchy problem has a unique solution. Some properties of this solution are studied, in particular, the finite dependence property and an $L^1$-estimate. |
| format | Article |
| id | doaj-art-6dc83f6f925141bb92079e466cf1c41e |
| institution | Kabale University |
| issn | 2072-9812 2409-8906 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Odesa National University of Technology |
| record_format | Article |
| series | Pracì Mìžnarodnogo Geometričnogo Centru |
| spelling | doaj-art-6dc83f6f925141bb92079e466cf1c41e2025-08-20T03:30:09ZengOdesa National University of TechnologyPracì Mìžnarodnogo Geometričnogo Centru2072-98122409-89062025-06-0118114315810.15673/pigc.v18i1.28492849Fundamental Solution for a New Class of Non-Archimedean Pseudo-Differential EquationsМарія Вікторівна Сердюк0Анатолій Наумович Кочубей1Інститут математики НАН УкраїниInstitute of MathematicsIn this paper we study a new class of pseudo-differential equations on functions of two $p$-adic variables. It is proved that the correspondent Cauchy problem has a unique solution. Some properties of this solution are studied, in particular, the finite dependence property and an $L^1$-estimate.https://journals.ontu.edu.ua/index.php/geometry/article/view/2849p-adic fieldpseudo-differential equationcauchy problem |
| spellingShingle | Марія Вікторівна Сердюк Анатолій Наумович Кочубей Fundamental Solution for a New Class of Non-Archimedean Pseudo-Differential Equations Pracì Mìžnarodnogo Geometričnogo Centru p-adic field pseudo-differential equation cauchy problem |
| title | Fundamental Solution for a New Class of Non-Archimedean Pseudo-Differential Equations |
| title_full | Fundamental Solution for a New Class of Non-Archimedean Pseudo-Differential Equations |
| title_fullStr | Fundamental Solution for a New Class of Non-Archimedean Pseudo-Differential Equations |
| title_full_unstemmed | Fundamental Solution for a New Class of Non-Archimedean Pseudo-Differential Equations |
| title_short | Fundamental Solution for a New Class of Non-Archimedean Pseudo-Differential Equations |
| title_sort | fundamental solution for a new class of non archimedean pseudo differential equations |
| topic | p-adic field pseudo-differential equation cauchy problem |
| url | https://journals.ontu.edu.ua/index.php/geometry/article/view/2849 |
| work_keys_str_mv | AT maríâvíktorívnaserdûk fundamentalsolutionforanewclassofnonarchimedeanpseudodifferentialequations AT anatolíjnaumovičkočubej fundamentalsolutionforanewclassofnonarchimedeanpseudodifferentialequations |