Energy decay rate of multidimensional inhomogeneous Landau–Lifshitz–Gilbert equation and Schrödinger map equation on the sphere
Abstract We consider the multidimensional dimensional inhomogeneous Landau–Lifshitz–Gilbert (ILLG) equation and its degenerate case, the Schrödinger map equation. We investigate the special solutions (under large initial values) and their energy property of the ILLG and Schrödinger map equations. Un...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-09-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-018-1795-4 |
| _version_ | 1818911855456813056 |
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| author | Penghong Zhong Chao Zhang Fengong Wu |
| author_facet | Penghong Zhong Chao Zhang Fengong Wu |
| author_sort | Penghong Zhong |
| collection | DOAJ |
| description | Abstract We consider the multidimensional dimensional inhomogeneous Landau–Lifshitz–Gilbert (ILLG) equation and its degenerate case, the Schrödinger map equation. We investigate the special solutions (under large initial values) and their energy property of the ILLG and Schrödinger map equations. Until now, we had not seen a paper presenting an explicit dynamic solution of the multidimensional ILLG. Using the stereographic method, an equivalent equation of ILLG is obtained. Based on this equivalent system, we obtain some exact solutions of the ILLG equation and present some implicit solutions of the Schrödinger map equation. Based on these solutions, by a careful estimation we give the decay rate of energy density. |
| first_indexed | 2024-12-19T23:05:20Z |
| format | Article |
| id | doaj.art-bf6e81dcaf4542648f125a791f8eeed6 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-19T23:05:20Z |
| publishDate | 2018-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-bf6e81dcaf4542648f125a791f8eeed62022-12-21T20:02:23ZengSpringerOpenAdvances in Difference Equations1687-18472018-09-012018112510.1186/s13662-018-1795-4Energy decay rate of multidimensional inhomogeneous Landau–Lifshitz–Gilbert equation and Schrödinger map equation on the spherePenghong Zhong0Chao Zhang1Fengong Wu2Department of Mathematics, Guangdong University of EducationDepartment of Mathematics, Guangdong University of EducationDepartment of Mathematics, Guangdong University of EducationAbstract We consider the multidimensional dimensional inhomogeneous Landau–Lifshitz–Gilbert (ILLG) equation and its degenerate case, the Schrödinger map equation. We investigate the special solutions (under large initial values) and their energy property of the ILLG and Schrödinger map equations. Until now, we had not seen a paper presenting an explicit dynamic solution of the multidimensional ILLG. Using the stereographic method, an equivalent equation of ILLG is obtained. Based on this equivalent system, we obtain some exact solutions of the ILLG equation and present some implicit solutions of the Schrödinger map equation. Based on these solutions, by a careful estimation we give the decay rate of energy density.http://link.springer.com/article/10.1186/s13662-018-1795-4Landau–Lifshitz–Gilbert equationSchrödinger map equationDecay rate |
| spellingShingle | Penghong Zhong Chao Zhang Fengong Wu Energy decay rate of multidimensional inhomogeneous Landau–Lifshitz–Gilbert equation and Schrödinger map equation on the sphere Advances in Difference Equations Landau–Lifshitz–Gilbert equation Schrödinger map equation Decay rate |
| title | Energy decay rate of multidimensional inhomogeneous Landau–Lifshitz–Gilbert equation and Schrödinger map equation on the sphere |
| title_full | Energy decay rate of multidimensional inhomogeneous Landau–Lifshitz–Gilbert equation and Schrödinger map equation on the sphere |
| title_fullStr | Energy decay rate of multidimensional inhomogeneous Landau–Lifshitz–Gilbert equation and Schrödinger map equation on the sphere |
| title_full_unstemmed | Energy decay rate of multidimensional inhomogeneous Landau–Lifshitz–Gilbert equation and Schrödinger map equation on the sphere |
| title_short | Energy decay rate of multidimensional inhomogeneous Landau–Lifshitz–Gilbert equation and Schrödinger map equation on the sphere |
| title_sort | energy decay rate of multidimensional inhomogeneous landau lifshitz gilbert equation and schrodinger map equation on the sphere |
| topic | Landau–Lifshitz–Gilbert equation Schrödinger map equation Decay rate |
| url | http://link.springer.com/article/10.1186/s13662-018-1795-4 |
| work_keys_str_mv | AT penghongzhong energydecayrateofmultidimensionalinhomogeneouslandaulifshitzgilbertequationandschrodingermapequationonthesphere AT chaozhang energydecayrateofmultidimensionalinhomogeneouslandaulifshitzgilbertequationandschrodingermapequationonthesphere AT fengongwu energydecayrateofmultidimensionalinhomogeneouslandaulifshitzgilbertequationandschrodingermapequationonthesphere |