Regularity of a Stochastic Fractional Delayed Reaction-Diffusion Equation Driven by Lévy Noise
The current paper is devoted to the regularity of the mild solution for a stochastic fractional delayed reaction-diffusion equation driven by Lévy space-time white noise. By the Banach fixed point theorem, the existence and uniqueness of the mild solution are proved in the proper working function sp...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/807459 |
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| _version_ | 1849306023545798656 |
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| author | Tianlong Shen Jianhua Huang Jin Li |
| author_facet | Tianlong Shen Jianhua Huang Jin Li |
| author_sort | Tianlong Shen |
| collection | DOAJ |
| description | The current paper is devoted to the regularity of the mild solution for a stochastic fractional delayed reaction-diffusion equation
driven by Lévy space-time white noise. By the Banach fixed point theorem, the existence and uniqueness of the mild solution are proved in the proper working function space which is affected by the delays. Furthermore, the time regularity and space regularity of the mild solution are established respectively. The main results show that both time regularity and space regularity of the mild solution depend on the regularity of initial value and the order of fractional operator. In particular, the time regularity is affected by the regularity of initial value with delays. |
| format | Article |
| id | doaj-art-3105d0f737674ee08b760920b44eae20 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-3105d0f737674ee08b760920b44eae202025-08-20T03:55:12ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/807459807459Regularity of a Stochastic Fractional Delayed Reaction-Diffusion Equation Driven by Lévy NoiseTianlong Shen0Jianhua Huang1Jin Li2Department of Mathematics, National University of Defense Technology, Changsha 410073, ChinaDepartment of Mathematics, National University of Defense Technology, Changsha 410073, ChinaDepartment of Mathematics, National University of Defense Technology, Changsha 410073, ChinaThe current paper is devoted to the regularity of the mild solution for a stochastic fractional delayed reaction-diffusion equation driven by Lévy space-time white noise. By the Banach fixed point theorem, the existence and uniqueness of the mild solution are proved in the proper working function space which is affected by the delays. Furthermore, the time regularity and space regularity of the mild solution are established respectively. The main results show that both time regularity and space regularity of the mild solution depend on the regularity of initial value and the order of fractional operator. In particular, the time regularity is affected by the regularity of initial value with delays.http://dx.doi.org/10.1155/2013/807459 |
| spellingShingle | Tianlong Shen Jianhua Huang Jin Li Regularity of a Stochastic Fractional Delayed Reaction-Diffusion Equation Driven by Lévy Noise Abstract and Applied Analysis |
| title | Regularity of a Stochastic Fractional Delayed Reaction-Diffusion Equation Driven by Lévy Noise |
| title_full | Regularity of a Stochastic Fractional Delayed Reaction-Diffusion Equation Driven by Lévy Noise |
| title_fullStr | Regularity of a Stochastic Fractional Delayed Reaction-Diffusion Equation Driven by Lévy Noise |
| title_full_unstemmed | Regularity of a Stochastic Fractional Delayed Reaction-Diffusion Equation Driven by Lévy Noise |
| title_short | Regularity of a Stochastic Fractional Delayed Reaction-Diffusion Equation Driven by Lévy Noise |
| title_sort | regularity of a stochastic fractional delayed reaction diffusion equation driven by levy noise |
| url | http://dx.doi.org/10.1155/2013/807459 |
| work_keys_str_mv | AT tianlongshen regularityofastochasticfractionaldelayedreactiondiffusionequationdrivenbylevynoise AT jianhuahuang regularityofastochasticfractionaldelayedreactiondiffusionequationdrivenbylevynoise AT jinli regularityofastochasticfractionaldelayedreactiondiffusionequationdrivenbylevynoise |