Self-similar singular solution of doubly singular parabolic equation with gradient absorption term
<p/> <p>We deal with the self-similar singular solution of doubly singular parabolic equation with a gradient absorption term <inline-formula><graphic file="1029-242X-2006-20438-i1.gif"/></inline-formula> for <inline-formula><graphic file="1029-2...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2006-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2006/20438 |
| _version_ | 1818576991142543360 |
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| author | Shi Peihu Wang Mingxin |
| author_facet | Shi Peihu Wang Mingxin |
| author_sort | Shi Peihu |
| collection | DOAJ |
| description | <p/> <p>We deal with the self-similar singular solution of doubly singular parabolic equation with a gradient absorption term <inline-formula><graphic file="1029-242X-2006-20438-i1.gif"/></inline-formula> for <inline-formula><graphic file="1029-242X-2006-20438-i2.gif"/></inline-formula>, <inline-formula><graphic file="1029-242X-2006-20438-i3.gif"/></inline-formula> and <inline-formula><graphic file="1029-242X-2006-20438-i4.gif"/></inline-formula> in <inline-formula><graphic file="1029-242X-2006-20438-i5.gif"/></inline-formula>. By shooting and phase plane methods, we prove that when <inline-formula><graphic file="1029-242X-2006-20438-i6.gif"/></inline-formula> there exists self-similar singular solution, while <inline-formula><graphic file="1029-242X-2006-20438-i7.gif"/></inline-formula> there is no any self-similar singular solution. In case of existence, the self-similar singular solution is the self-similar very singular solutions which have compact support. Moreover, the interface relation is obtained.</p> |
| first_indexed | 2024-12-16T06:22:48Z |
| format | Article |
| id | doaj.art-04f770b94fbd411e8e86d59005459f96 |
| institution | Directory Open Access Journal |
| issn | 1025-5834 1029-242X |
| language | English |
| last_indexed | 2024-12-16T06:22:48Z |
| publishDate | 2006-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-04f770b94fbd411e8e86d59005459f962022-12-21T22:41:05ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2006-01-012006120438Self-similar singular solution of doubly singular parabolic equation with gradient absorption termShi PeihuWang Mingxin<p/> <p>We deal with the self-similar singular solution of doubly singular parabolic equation with a gradient absorption term <inline-formula><graphic file="1029-242X-2006-20438-i1.gif"/></inline-formula> for <inline-formula><graphic file="1029-242X-2006-20438-i2.gif"/></inline-formula>, <inline-formula><graphic file="1029-242X-2006-20438-i3.gif"/></inline-formula> and <inline-formula><graphic file="1029-242X-2006-20438-i4.gif"/></inline-formula> in <inline-formula><graphic file="1029-242X-2006-20438-i5.gif"/></inline-formula>. By shooting and phase plane methods, we prove that when <inline-formula><graphic file="1029-242X-2006-20438-i6.gif"/></inline-formula> there exists self-similar singular solution, while <inline-formula><graphic file="1029-242X-2006-20438-i7.gif"/></inline-formula> there is no any self-similar singular solution. In case of existence, the self-similar singular solution is the self-similar very singular solutions which have compact support. Moreover, the interface relation is obtained.</p>http://www.journalofinequalitiesandapplications.com/content/2006/20438 |
| spellingShingle | Shi Peihu Wang Mingxin Self-similar singular solution of doubly singular parabolic equation with gradient absorption term Journal of Inequalities and Applications |
| title | Self-similar singular solution of doubly singular parabolic equation with gradient absorption term |
| title_full | Self-similar singular solution of doubly singular parabolic equation with gradient absorption term |
| title_fullStr | Self-similar singular solution of doubly singular parabolic equation with gradient absorption term |
| title_full_unstemmed | Self-similar singular solution of doubly singular parabolic equation with gradient absorption term |
| title_short | Self-similar singular solution of doubly singular parabolic equation with gradient absorption term |
| title_sort | self similar singular solution of doubly singular parabolic equation with gradient absorption term |
| url | http://www.journalofinequalitiesandapplications.com/content/2006/20438 |
| work_keys_str_mv | AT shipeihu selfsimilarsingularsolutionofdoublysingularparabolicequationwithgradientabsorptionterm AT wangmingxin selfsimilarsingularsolutionofdoublysingularparabolicequationwithgradientabsorptionterm |