On Stability of Regular Precession of an Asymmetrical Gyroscope in a Critical Case of the Fourth-Order Resonance

2018 ◽  
Vol 481 (2) ◽  
pp. 151-155
Author(s):  
A. Markeev ◽  
◽  
Keyword(s):  
Fourth Order ◽  
Critical Case ◽  
Order Resonance ◽  
Regular Precession

scholarly journals Asymptotic theory for a critical case for a general fourth-order differential equation

1998 ◽  
Vol 21 (3) ◽  
pp. 479-488
Author(s):  
A. S. A. Al-Hammadi
Keyword(s):  
Differential Equation ◽  
Fourth Order ◽  
Critical Case ◽  
Asymptotic Theory ◽  
Order Differential Equation ◽  
Fourth Order Equations ◽  
Fourth Order Differential Equation

In this paper we identify a relation between the coefficients that represents a critical case for general fourth-order equations. We obtained the forms of solutions under this critical case.

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.

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