Blow-up with mass concentration for the long-wave unstable thin-film equation

For a family of long-wave unstable thin-film equations, we prove existence of non-negative weak solutions blowing-up in a finite time. Specifically, building these solutions from initial data with negative energy, we show that their -norms go to infinity as . In addition, using the Bourgain's t...

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Bibliographic Details
Published in:Applicable analysis 2016-05, Vol.95 (5), p.944-962
Main Authors: Chugunova, Marina, Taranets, Roman M.
Format: Article
Language:English
Subjects:
Applied mathematics
blow-up
Buildings
Infinity
long-wave instability
mass concentration
Mathematical analysis
Thin films
thin-film equation
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Summary:For a family of long-wave unstable thin-film equations, we prove existence of non-negative weak solutions blowing-up in a finite time. Specifically, building these solutions from initial data with negative energy, we show that their -norms go to infinity as . In addition, using the Bourgain's type approach, we obtain qualitative information about the blow-up and prove mass concentration phenomenon.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2015.1047829