scholarly journals Steady state non-Newtonian flow with strain rate dependent viscosity in domains with cylindrical outlets to infinity

2021 ◽  
Vol 26 (6) ◽  
pp. 1166-1199
Author(s):  
Grigory Panasenko ◽  
Konstantin Pileckas ◽  
Bogdan Vernescu
Keyword(s):  
Fixed Point ◽  
Unbounded Domains ◽  
Regularity Of Solutions ◽  
Banach Fixed Point Theorem ◽  
Newtonian Flow ◽  
Rate Dependent ◽  
The Stability ◽  
Dependent Viscosity ◽  
Stability Of The Solution ◽  
Poiseuille Flows

The paper deals with a stationary non-Newtonian flow of a viscous fluid in unbounded domains with cylindrical outlets to infinity. The viscosity is assumed to be smoothly dependent on the gradient of the velocity. Applying the generalized Banach fixed point theorem, we prove the existence, uniqueness and high order regularity of solutions stabilizing in the outlets to the prescribed quasi-Poiseuille flows. Varying the limit quasi-Poiseuille flows, we prove the stability of the solution.

EXISTENCE AND REGULARITY OF SOLUTIONS AND THE STABILITY OF THE REST STATE FOR FLUIDS WITH SHEAR DEPENDENT VISCOSITY

1995 ◽  
Vol 05 (06) ◽  
pp. 789-812 ◽  
Author(s):  
J. MÁLEK ◽  
K.R. RAJAGOPAL ◽  
M. RŮŽIČKA
Keyword(s):  
Existence Of Solutions ◽  
Regularity Of Solutions ◽  
Small Data ◽  
Fluid Models ◽  
Rest State ◽  
Convergence Almost Everywhere ◽  
Shear Dependent Viscosity ◽  
Almost Everywhere ◽  
The Stability ◽  
Dependent Viscosity

In this paper we clarify and discuss some subtle features concerning the non-Newtonian fluid models which were considered by Málek, Nečas and Růžička.19 We establish new results regarding the stability of the rest state of mechanically isolated flows of such non-Newtonian fluids for arbitrary initial disturbances. We also discuss some results concerning the existence and regularity of solutions for small data. These results are based on a new method, giving convergence almost everywhere of approximations of gradients from boundedness of fraction of the L2-norm of the second and first derivatives, developed by Nečas to study existence of solutions (global in time) to a class of partial differential equations.

scholarly journals Some qualitative properties of nonlinear fractional integro-differential equations of variable order

2021 ◽  
Vol 11 (3) ◽  
pp. 68-78
Author(s):  
Ahmed Refice ◽  
Mohammed Said Souid ◽  
Ali Yakar
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Banach Fixed Point Theorem ◽  
Variable Order ◽  
Qualitative Properties ◽  
Piecewise Constant ◽  
Fractional Differential ◽  
The Stability ◽  
Uniqueness Criteria

The existence-uniqueness criteria of nonlinear fractional integro-differential equations of variable order with multiterm boundary value conditions are considered in this work. By utilizing the concepts of generalized intervals combined with the piecewise constant functions, we transform our problem into usual Caputo’s fractional differential equations of constant order. We develop the necessary criteria for assuring the solution's existence and uniqueness by applying Schauder and Banach fixed point theorem. We also examine the stability of the derived solution in the Ulam-Hyers-Rassias (UHR) sense and provide an example to demonstrate the credibility of the results.

scholarly journals A Study of Stability of First-Order Delay Differential Equations Using Fixed Point Theorem Banach

2019 ◽  
pp. 2719-2724
Author(s):  
Zaid A.A. Mahdi Monje ◽  
Buthainah A.A. Ahmed
Keyword(s):  
Fixed Point ◽  
Asymptotic Stability ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Delay Differential Equations ◽  
Zero Solution ◽  
Banach Fixed Point Theorem ◽  
First Order ◽  
The Stability ◽  
Delay Differential

     In this paper we investigate the stability and asymptotic stability of the zero solution for the first order delay differential equation      where the delay is variable and by using Banach fixed point theorem. We give new conditions to ensure the stability and asymptotic stability of the zero solution of this equation.

Stability of a Non-Newtonian Fluid in a Channel With Heat Transfer

2003 ◽  
Author(s):  
Coskun Ozalp ◽  
Ahmet Pinarbasi
Keyword(s):  
Eigenvalue Problem ◽  
Base Flow ◽  
Marginal Stability ◽  
Flow Equations ◽  
Rate Dependent ◽  
Wide Range ◽  
Qz Algorithm ◽  
Generalized Matrix ◽  
The Stability ◽  
Dependent Viscosity

In this paper the linear stability of plane Poiseuille flow is studied for a non-Newtonian liquid having an exponential viscosity-temperature dependence. Non-Newtonian behavior of the fluid is modeled through Carreau rheological equation. Channels walls are kept at constant but different temperatures. Steady base flow equations and equations describing the evolution of small, two-dimensional disturbances are derived and solved numerically. The stability problem is formulated as an eigenvalue problem for a set of ordinary idfferential equations. Discritization is performed using a pseudospectral technique based on Chebyshev polynomials expanisons. The resulting generalized matrix eigenvalue problem is solved using the QZ algorithm. The results presenting the influence of temperature and shear-rate dependent viscosity on the stability are given in the form of marginal stability curves for a wide range of flow and fluid dimensionless parameters, including channel wall temperature difference ΔT, material time constant λ and power-law index n.

A fixed point approach to the stability of sextic Lie *-derivations

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4933-4944
Author(s):  
Dongseung Kang ◽  
Heejeong Koh
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Single Case ◽  
Fixed Point Method ◽  
Point Method ◽  
Fixed Point Approach ◽  
The Stability ◽  
The Given ◽  
Lie Derivations

We obtain a general solution of the sextic functional equation f (ax+by)+ f (ax-by)+ f (bx+ay)+ f (bx-ay) = (ab)2(a2 + b2)[f(x+y)+f(x-y)] + 2(a2-b2)(a4-b4)[f(x)+f(y)] and investigate the stability of sextic Lie *-derivations associated with the given functional equation via fixed point method. Also, we present a counterexample for a single case.

scholarly journals A Fractional SAIDR Model in the Frame of Atangana–Baleanu Derivative

2021 ◽  
Vol 5 (2) ◽  
pp. 32
Author(s):  
Esmehan Uçar ◽  
Sümeyra Uçar ◽  
Fırat Evirgen ◽  
Necati Özdemir
Keyword(s):  
Existence And Uniqueness ◽  
Laplace Transformation ◽  
Cell Phones ◽  
Mobile Network ◽  
The Other ◽  
Banach Fixed Point Theorem ◽  
Propagation Models ◽  
Computer Worms ◽  
Computer Viruses ◽  
The Stability

It is possible to produce mobile phone worms, which are computer viruses with the ability to command the running of cell phones by taking advantage of their flaws, to be transmitted from one device to the other with increasing numbers. In our day, one of the services to gain currency for circulating these malignant worms is SMS. The distinctions of computers from mobile devices render the existing propagation models of computer worms unable to start operating instantaneously in the mobile network, and this is particularly valid for the SMS framework. The susceptible–affected–infectious–suspended–recovered model with a classical derivative (abbreviated as SAIDR) was coined by Xiao et al., (2017) in order to correctly estimate the spread of worms by means of SMS. This study is the first to implement an Atangana–Baleanu (AB) derivative in association with the fractional SAIDR model, depending upon the SAIDR model. The existence and uniqueness of the drinking model solutions together with the stability analysis are shown through the Banach fixed point theorem. The special solution of the model is investigated using the Laplace transformation and then we present a set of numeric graphics by varying the fractional-order θ with the intention of showing the effectiveness of the fractional derivative.

scholarly journals On the stability of set-valued functional equations with the fixed point alternative

2012 ◽  
Vol 2012 (1) ◽  
pp. 81 ◽  
Author(s):  
Hassan Kenary ◽  
Hamid Rezaei ◽  
Yousof Gheisari ◽  
Choonkil Park
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
The Stability

scholarly journals On Almost Automorphic Mild Solutions for Nonautonomous Stochastic Evolution Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Jing Cui ◽  
Litan Yan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Banach Fixed Point Theorem ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Almost Automorphic ◽  
Composition Theorem

We consider a class of nonautonomous stochastic evolution equations in real separable Hilbert spaces. We establish a new composition theorem for square-mean almost automorphic functions under non-Lipschitz conditions. We apply this new composition theorem as well as intermediate space techniques, Krasnoselskii fixed point theorem, and Banach fixed point theorem to investigate the existence of square-mean almost automorphic mild solutions. Some known results are generalized and improved.

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