Global existence blow up and extinction for a class of thin-film equation

2016 ◽  
Vol 147 ◽  
pp. 96-109 ◽  
Author(s):  
Qingwei Li ◽  
Wenjie Gao ◽  
Yuzhu Han
Keyword(s):  
Thin Film ◽  
Global Existence ◽  
Blow Up ◽  
Thin Film Equation

scholarly journals Global existence for a thin film equation with subcritical mass

2017 ◽  
Vol 22 (4) ◽  
pp. 1461-1492 ◽  
Author(s):  
Jian-Guo Liu ◽  
◽  
Jinhuan Wang ◽  
Keyword(s):  
Thin Film ◽  
Global Existence ◽  
Thin Film Equation

scholarly journals Blowup and dissipation in a critical-case unstable thin film equation

2004 ◽  
Vol 15 (2) ◽  
pp. 223-256 ◽  
Author(s):  
T. P. WITELSKI ◽  
A. J. BERNOFF ◽  
A. L. BERTOZZI
Keyword(s):  
Thin Film ◽  
Fourth Order ◽  
Critical Case ◽  
Blow Up ◽  
Critical Mass ◽  
Similarity Solutions ◽  
Fluid Layers ◽  
Parabolic Pde ◽  
Thin Film Equation ◽  
Order Degenerate

We study the dynamics of dissipation and blow-up in a critical-case unstable thin film equation. The governing equation is a nonlinear fourth-order degenerate parabolic PDE derived from a generalized model for lubrication flows of thin viscous fluid layers on solid surfaces. %For a special balance between %destabilizing second-order terms and regularizing fourth-order terms, There is a critical mass for blow-up and a rich set of dynamics including families of similarity solutions for finite-time blow-up and infinite-time spreading. The structure and stability of the steady-states and the compactly-supported similarity solutions is studied.

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

2015 ◽  
Vol 95 (5) ◽  
pp. 944-962 ◽  
Author(s):  
Marina Chugunova ◽  
Roman M. Taranets
Keyword(s):  
Thin Film ◽  
Mass Concentration ◽  
Blow Up ◽  
Long Wave ◽  
Thin Film Equation
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