Singularly perturbed periodic parabolic equations with alternating boundary layer type solutions
<p>We consider a class of singularly perturbed parabolic equations for which the degenerate equations obtained by setting the small parameter equal to zero are algebraic equations that have several roots. We study boundary layer type solutions that, as time increases, periodically go through t...
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| Format: | Article |
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| Language: | English |
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Wiley
2006-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://www.hindawi.com/GetArticle.aspx?doi=10.1155/AAA/2006/52856 |
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| description | <p>We consider a class of singularly perturbed parabolic equations for which the degenerate equations obtained by setting the small parameter equal to zero are algebraic equations that have several roots. We study boundary layer type solutions that, as time increases, periodically go through two fairly long lasting stages with extremely fast transitions in between. During one of these stages the solution outside the boundary layer is close to one of the roots of the degenerate (reduced) equation, while during the other stage the solution is close to the other root. Such equations may be used as models for bio-switches where the transitions between various stationary states of biological systems are initiated by comparatively slow changes within the systems.</p> |
| format | Article |
| id | doaj-art-c1e9a5c370c94112b774be7e258a9bda |
| institution | Kabale University |
| issn | 1085-3375 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-c1e9a5c370c94112b774be7e258a9bda2025-02-03T05:46:31ZengWileyAbstract and Applied Analysis1085-33752006-01-012006Singularly perturbed periodic parabolic equations with alternating boundary layer type solutions<p>We consider a class of singularly perturbed parabolic equations for which the degenerate equations obtained by setting the small parameter equal to zero are algebraic equations that have several roots. We study boundary layer type solutions that, as time increases, periodically go through two fairly long lasting stages with extremely fast transitions in between. During one of these stages the solution outside the boundary layer is close to one of the roots of the degenerate (reduced) equation, while during the other stage the solution is close to the other root. Such equations may be used as models for bio-switches where the transitions between various stationary states of biological systems are initiated by comparatively slow changes within the systems.</p>http://www.hindawi.com/GetArticle.aspx?doi=10.1155/AAA/2006/52856 |
| spellingShingle | Singularly perturbed periodic parabolic equations with alternating boundary layer type solutions Abstract and Applied Analysis |
| title | Singularly perturbed periodic parabolic equations with alternating boundary layer type solutions |
| title_full | Singularly perturbed periodic parabolic equations with alternating boundary layer type solutions |
| title_fullStr | Singularly perturbed periodic parabolic equations with alternating boundary layer type solutions |
| title_full_unstemmed | Singularly perturbed periodic parabolic equations with alternating boundary layer type solutions |
| title_short | Singularly perturbed periodic parabolic equations with alternating boundary layer type solutions |
| title_sort | singularly perturbed periodic parabolic equations with alternating boundary layer type solutions |
| url | http://www.hindawi.com/GetArticle.aspx?doi=10.1155/AAA/2006/52856 |