Self-similar singular solution of doubly singular parabolic equation with gradient absorption term

• Main Authors: Shi Peihu, Wang Mingxin
• Format: Article
• Language: English
• Published: SpringerOpen 2006-01-01
• Series: Journal of Inequalities and Applications
• Online Access: http://www.journalofinequalitiesandapplications.com/content/2006/20438

<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>