scholarly journals A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids

2011 ◽  
Vol 467 (2134) ◽  
pp. 3033-3034
Author(s):  
Mihai Mihăilescu ◽  
Vicenţiu Rădulescu
Keyword(s):  
Electrorheological Fluids ◽  
Multiplicity Result ◽  
Degenerate Problem ◽  
Nonlinear Degenerate

scholarly journals A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids

2006 ◽  
Vol 462 (2073) ◽  
pp. 2625-2641 ◽  
Author(s):  
Mihai Mihăilescu ◽  
Vicenţiu Rădulescu
Keyword(s):  
Boundary Value Problem ◽  
Sobolev Spaces ◽  
Variable Exponent ◽  
Electrorheological Fluids ◽  
Mountain Pass Lemma ◽  
Multiplicity Result ◽  
Smooth Bounded Domain ◽  
Degenerate Problem ◽  
Laplace Type ◽  
Nonlinear Degenerate

We study the boundary value problem in , u =0 on , where is a smooth bounded domain in and is a -Laplace type operator, with . We prove that if λ is large enough then there exist at least two non-negative weak solutions. Our approach relies on the variable exponent theory of generalized Lebesgue–Sobolev spaces, combined with adequate variational methods and a variant of the Mountain Pass lemma.

scholarly journals Entropy solutions for an adaptive fourth-order nonlinear degenerate problem for noise removal

2021 ◽  
Vol 6 (4) ◽  
pp. 3974-3995
Author(s):  
Abdelgader Siddig ◽  
◽  
Zhichang Guo ◽  
Zhenyu Zhou ◽  
Boying Wu ◽  
...  
Keyword(s):  
Fourth Order ◽  
Noise Removal ◽  
Entropy Solutions ◽  
Degenerate Problem ◽  
Nonlinear Degenerate

scholarly journals Existence results for nonlinear degenerate elliptic equations with lower order terms

2020 ◽  
Vol 10 (1) ◽  
pp. 301-310
Author(s):  
Weilin Zou ◽  
Xinxin Li
Keyword(s):  
Lower Order ◽  
Elliptic Equations ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Regularity Of Solutions ◽  
Degenerate Elliptic Equations ◽  
Degenerate Elliptic ◽  
Initial Boundary Value ◽  
Lower Order Terms ◽  
Nonlinear Degenerate

Abstract In this paper, we prove the existence and regularity of solutions of the homogeneous Dirichlet initial-boundary value problem for a class of degenerate elliptic equations with lower order terms. The results we obtained here, extend some existing ones of [2, 9, 11] in some sense.

Coating of Polyaniline with an Insulating Polymer to Improve the Power Efficiency of Electrorheological Fluids

1999 ◽  
Vol 13 (14n16) ◽  
pp. 1931-1939 ◽  
Author(s):  
J. Akhavan ◽  
K. Slack ◽  
V. Wise ◽  
H. Block
Keyword(s):  
Power Efficiency ◽  
Electrorheological Fluids ◽  
Emeraldine Base ◽  
Heavy Duty ◽  
Base Form ◽  
Static Yield ◽  
High Fields ◽  
Er Fluids ◽  
Er Fluid ◽  
A Current

Currents drawn under high fields often present practical limitations to electrorheological (ER) fluids usefulness. For heavy-duty applications where large torques have to be transmitted, the power consumption of a ER fluid can be considerable, and for such uses a current density of ~100μ A cm -2 is often taken as a practical upper limit. This investigation was conducted into designing a fluid which has little extraneous conductance and therefore would demand less current. Selected semi-conducting polymers provide effective substrates for ER fluids. Such polymers are soft insoluble powdery materials with densities similar to dispersing agents used in ER formulations. Polyaniline is a semi-conducting polymer and can be used as an effective ER substrate in its emeraldine base form. In order to provide an effective ER fluid which requires less current polyaniline was coated with an insulating polymer. The conditions for coating was established for lauryl and methyl methacrylate. Results from static yield measurements indicate that ER fluids containing coated polyaniline required less current than uncoated polyaniline i.e. 0.5μ A cm -2. The generic type of coating was also found to be important.

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