Solution of two-dimensional problems of filtration with a limiting gradient by the method of small parameter

1968 ◽  
Vol 32 (5) ◽  
pp. 872-884 ◽  
Author(s):  
V.M. Entov ◽  
R.L. Salganik
Keyword(s):  
Small Parameter ◽  
Two Dimensional ◽  
Method Of Small Parameter

Pulsatile pipe flow pseudoplastic materials; The flow enhancement for Re ≪ 1

1983 ◽  
Vol 48 (6) ◽  
pp. 1579-1587 ◽  
Author(s):  
Ondřej Wein
Keyword(s):  
Small Parameter ◽  
Pipe Flow ◽  
Quantitative Estimation ◽  
Reynolds Numbers ◽  
Power Law Model ◽  
Viscosity Function ◽  
Small Reynolds Numbers ◽  
Title Problem ◽  
Flow Enhancement ◽  
Method Of Small Parameter

Solution of the title problem for the power-law model of viscosity function is constructed by the method of small parameter in the region of small Reynolds numbers. The main result of the paper is a quantitative estimation of the values of Re, when the influence of inertia on flow enhancement may be quite neglected.

AVERAGING PRINCIPLE FOR QUASI-LINEAR PARABOLIC PDEs AND RELATED DIFFUSION PROCESSES

2012 ◽  
Vol 12 (01) ◽  
pp. 1150008 ◽  
Author(s):  
MARK FREIDLIN ◽  
LEONID KORALOV
Keyword(s):  
Small Parameter ◽  
Diffusion Processes ◽  
First Integral ◽  
Second Order ◽  
Averaging Principle ◽  
Two Dimensional ◽  
Parabolic Pdes ◽  
Dimensional Flow ◽  
Linear Perturbations ◽  
Two Dimensional Flow

Quasi-linear perturbations of a two-dimensional flow with a first integral and the corresponding parabolic PDEs with a small parameter at the second-order derivatives are considered in this paper.

Extension of the Prandtl–Batchelor theorem to three-dimensional flows slowly varying in one direction

2010 ◽  
Vol 654 ◽  
pp. 351-361 ◽  
Author(s):  
M. SANDOVAL ◽  
S. CHERNYSHENKO
Keyword(s):  
Flow Field ◽  
Small Parameter ◽  
Order Approximation ◽  
Three Dimensional ◽  
Inviscid Limit ◽  
Two Dimensional ◽  
Leading Order ◽  
Dimensional Flow ◽  
Two Dimensional Flow

According to the Prandtl–Batchelor theorem for a steady two-dimensional flow with closed streamlines in the inviscid limit the vorticity becomes constant in the region of closed streamlines. This is not true for three-dimensional flows. However, if the variation of the flow field along one direction is slow then it is possible to expand the solution in terms of a small parameter characterizing the rate of variation of the flow field in that direction. Then in the leading-order approximation the projections of the streamlines onto planes perpendicular to that direction can be closed. Under these circumstances the extension of the Prandtl–Batchelor theorem is obtained. The resulting equations turned out to be a three-dimensional analogue of the equations of the quasi-cylindrical approximation.

Averaging of a nonlinear bipolar model with phase transition and oscillating external forces

2015 ◽  
Vol 21 (2) ◽  
Author(s):  
Theodore Tachim Medjo
Keyword(s):  
Phase Transition ◽  
Small Parameter ◽  
Global Attractor ◽  
Bounded Domain ◽  
External Force ◽  
Two Dimensional ◽  
External Forces ◽  
Uniform Global Attractor

AbstractIn this article, we consider a non-autonomous nonlinear bipolar with phase transition in a two-dimensional bounded domain. We assume that the external force is singularly oscillating and depends on a small parameter ϵ. We prove the existence of the uniform global attractor 𝒜

On the reducibility of two-dimensional linear quasi-periodic systems with small parameter

2014 ◽  
Vol 35 (7) ◽  
pp. 2334-2352 ◽  
Author(s):  
JUNXIANG XU ◽  
XUEZHU LU
Keyword(s):  
Differential Equations ◽  
Small Parameter ◽  
Lebesgue Measure ◽  
Periodic System ◽  
Coefficient Matrix ◽  
Periodic Systems ◽  
Two Dimensional ◽  
Constant Matrix ◽  
Small Parameters ◽  
Real Analytic

In this paper we consider a linear real analytic quasi-periodic system of two differential equations, whose coefficient matrix analytically depends on a small parameter and closes to constant. Under some non-resonance conditions about the basic frequencies and the eigenvalues of the constant matrix and without any non-degeneracy assumption of the small parameter, we prove that the system is reducible for most of the sufficiently small parameters in the sense of the Lebesgue measure.

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