The Step-Type Contrast Structure for High Dimensional Tikhonov System with Neumann Boundary Conditions
We investigate the step-type contrast structure for high dimensional Tikhonov system with Neumann boundary conditions. We not only propose a key condition with the existence of the number of mutually independent first integrals under which there exists a step-type contrast structure, but also determ...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2016/4569198 |
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| _version_ | 1832556115155484672 |
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| author | Aifeng Wang Mingkang Ni |
| author_facet | Aifeng Wang Mingkang Ni |
| author_sort | Aifeng Wang |
| collection | DOAJ |
| description | We investigate the step-type contrast structure for high dimensional Tikhonov system with Neumann boundary conditions. We not only propose a key condition with the existence of the number of mutually independent first integrals under which there exists a step-type contrast structure, but also determine where an internal transition time is. Using the method of boundary function, we construct the formal asymptotic solution and give the analytical expression for the higher order terms. At the same time, the uniformly valid asymptotic expansion and the existence of such an available step-type contrast structure are obtained by sewing connection method. |
| format | Article |
| id | doaj-art-559d8b1acaf34bfe956ba5750f57bbac |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-559d8b1acaf34bfe956ba5750f57bbac2025-02-03T05:46:20ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2016-01-01201610.1155/2016/45691984569198The Step-Type Contrast Structure for High Dimensional Tikhonov System with Neumann Boundary ConditionsAifeng Wang0Mingkang Ni1School of Mathematical Science, Huaiyin Normal University, Huai’an 223001, ChinaDepartment of Mathematics, East China Normal University, Shanghai 200062, ChinaWe investigate the step-type contrast structure for high dimensional Tikhonov system with Neumann boundary conditions. We not only propose a key condition with the existence of the number of mutually independent first integrals under which there exists a step-type contrast structure, but also determine where an internal transition time is. Using the method of boundary function, we construct the formal asymptotic solution and give the analytical expression for the higher order terms. At the same time, the uniformly valid asymptotic expansion and the existence of such an available step-type contrast structure are obtained by sewing connection method.http://dx.doi.org/10.1155/2016/4569198 |
| spellingShingle | Aifeng Wang Mingkang Ni The Step-Type Contrast Structure for High Dimensional Tikhonov System with Neumann Boundary Conditions Discrete Dynamics in Nature and Society |
| title | The Step-Type Contrast Structure for High Dimensional Tikhonov System with Neumann Boundary Conditions |
| title_full | The Step-Type Contrast Structure for High Dimensional Tikhonov System with Neumann Boundary Conditions |
| title_fullStr | The Step-Type Contrast Structure for High Dimensional Tikhonov System with Neumann Boundary Conditions |
| title_full_unstemmed | The Step-Type Contrast Structure for High Dimensional Tikhonov System with Neumann Boundary Conditions |
| title_short | The Step-Type Contrast Structure for High Dimensional Tikhonov System with Neumann Boundary Conditions |
| title_sort | step type contrast structure for high dimensional tikhonov system with neumann boundary conditions |
| url | http://dx.doi.org/10.1155/2016/4569198 |
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