Stability of Exact and Discrete Energy for Non-Fickian Reaction-Diffusion Equations with a Variable Delay
This paper is concerned with the stability of non-Fickian reaction-diffusion equations with a variable delay. It is shown that the perturbation of the energy function of the continuous problems decays exponentially, which provides a more accurate and convenient way to express the rate of decay of en...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/840573 |
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| _version_ | 1832553206865985536 |
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| author | Dongfang Li Chao Tong Jinming Wen |
| author_facet | Dongfang Li Chao Tong Jinming Wen |
| author_sort | Dongfang Li |
| collection | DOAJ |
| description | This paper is concerned with the stability of non-Fickian reaction-diffusion equations with a variable delay. It is shown that the perturbation of the energy function of the continuous problems decays exponentially, which provides a more accurate and convenient way to express the rate of decay of energy. Then, we prove that the proposed numerical methods are sufficient to preserve energy stability of the continuous problems. We end the paper with some numerical experiments on a biological model to confirm the theoretical results. |
| format | Article |
| id | doaj-art-92544e5d048d409f932eb117dc128b50 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-92544e5d048d409f932eb117dc128b502025-02-03T05:55:16ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/840573840573Stability of Exact and Discrete Energy for Non-Fickian Reaction-Diffusion Equations with a Variable DelayDongfang Li0Chao Tong1Jinming Wen2School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, ChinaSchool of Computer Science and Engineering, Beihang University, Beijing 100191, ChinaDepartment of Mathematics and Statistics, McGill University, Montreal, QC, H3A 2K6, CanadaThis paper is concerned with the stability of non-Fickian reaction-diffusion equations with a variable delay. It is shown that the perturbation of the energy function of the continuous problems decays exponentially, which provides a more accurate and convenient way to express the rate of decay of energy. Then, we prove that the proposed numerical methods are sufficient to preserve energy stability of the continuous problems. We end the paper with some numerical experiments on a biological model to confirm the theoretical results.http://dx.doi.org/10.1155/2014/840573 |
| spellingShingle | Dongfang Li Chao Tong Jinming Wen Stability of Exact and Discrete Energy for Non-Fickian Reaction-Diffusion Equations with a Variable Delay Abstract and Applied Analysis |
| title | Stability of Exact and Discrete Energy for Non-Fickian Reaction-Diffusion Equations with a Variable Delay |
| title_full | Stability of Exact and Discrete Energy for Non-Fickian Reaction-Diffusion Equations with a Variable Delay |
| title_fullStr | Stability of Exact and Discrete Energy for Non-Fickian Reaction-Diffusion Equations with a Variable Delay |
| title_full_unstemmed | Stability of Exact and Discrete Energy for Non-Fickian Reaction-Diffusion Equations with a Variable Delay |
| title_short | Stability of Exact and Discrete Energy for Non-Fickian Reaction-Diffusion Equations with a Variable Delay |
| title_sort | stability of exact and discrete energy for non fickian reaction diffusion equations with a variable delay |
| url | http://dx.doi.org/10.1155/2014/840573 |
| work_keys_str_mv | AT dongfangli stabilityofexactanddiscreteenergyfornonfickianreactiondiffusionequationswithavariabledelay AT chaotong stabilityofexactanddiscreteenergyfornonfickianreactiondiffusionequationswithavariabledelay AT jinmingwen stabilityofexactanddiscreteenergyfornonfickianreactiondiffusionequationswithavariabledelay |