p-Adic Fractional Pseudodifferential Equations and Sobolev Type Spaces over p-Adic Fields
In this paper, we study the solutions of the pseudodifferential equations of type Dα u=v over p-adic field ℚp, where Dα is a p-adic fractional pseudodifferential operator. If v is a Bruhat-Schwartz function, then there exists a distribution Eα, a fundamental solution, such that u=Eα*v is a solution....
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2013/635690 |
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| author | Bo Wu |
| author_facet | Bo Wu |
| author_sort | Bo Wu |
| collection | DOAJ |
| description | In this paper, we study the solutions of the pseudodifferential equations of type Dα u=v over p-adic field ℚp, where Dα is a p-adic fractional pseudodifferential operator. If v is a Bruhat-Schwartz function, then there exists a distribution Eα, a fundamental solution, such that u=Eα*v is a solution. We also show that the solution u belongs to a certain Sobolev space. Furthermore, we give conditions for the continuity and uniqueness of u. |
| format | Article |
| id | doaj-art-171547012dd545df99cd98552980f8a1 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-171547012dd545df99cd98552980f8a12025-02-03T06:11:28ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2013-01-01201310.1155/2013/635690635690p-Adic Fractional Pseudodifferential Equations and Sobolev Type Spaces over p-Adic FieldsBo Wu0Department of Applied Mathematics, Nanjing University of Finance & Economics, Nanjing 210023, ChinaIn this paper, we study the solutions of the pseudodifferential equations of type Dα u=v over p-adic field ℚp, where Dα is a p-adic fractional pseudodifferential operator. If v is a Bruhat-Schwartz function, then there exists a distribution Eα, a fundamental solution, such that u=Eα*v is a solution. We also show that the solution u belongs to a certain Sobolev space. Furthermore, we give conditions for the continuity and uniqueness of u.http://dx.doi.org/10.1155/2013/635690 |
| spellingShingle | Bo Wu p-Adic Fractional Pseudodifferential Equations and Sobolev Type Spaces over p-Adic Fields Discrete Dynamics in Nature and Society |
| title | p-Adic Fractional Pseudodifferential Equations and Sobolev Type Spaces over p-Adic Fields |
| title_full | p-Adic Fractional Pseudodifferential Equations and Sobolev Type Spaces over p-Adic Fields |
| title_fullStr | p-Adic Fractional Pseudodifferential Equations and Sobolev Type Spaces over p-Adic Fields |
| title_full_unstemmed | p-Adic Fractional Pseudodifferential Equations and Sobolev Type Spaces over p-Adic Fields |
| title_short | p-Adic Fractional Pseudodifferential Equations and Sobolev Type Spaces over p-Adic Fields |
| title_sort | p adic fractional pseudodifferential equations and sobolev type spaces over p adic fields |
| url | http://dx.doi.org/10.1155/2013/635690 |
| work_keys_str_mv | AT bowu padicfractionalpseudodifferentialequationsandsobolevtypespacesoverpadicfields |