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- Almqvist, Andreas, et al.
(författare)
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Homogenization of the unstationary incompressible Reynolds equation
- 2007
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Ingår i: Tribology International. - : Elsevier BV. - 0301-679X .- 1879-2464. ; 40:9, s. 1344-1350
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Tidskriftsartikel (refereegranskat)abstract
- This paper is devoted to the effects of surface roughness during hydrodynamic lubrication. In the numerical analysis a very fine mesh is needed to resolve the surface roughness, suggesting some type of averaging. A rigorous way to do this is to use the general theory of homogenization. In most works about the influence of surface roughness, it is assumed that only the stationary surface is rough. This means that the governing Reynolds type equation does not involve time. However, recently, homogenization was successfully applied to analyze a situation where both surfaces are rough and the lubricant is assumed to have constant bulk modulus. In this paper we will consider a case where both surfaces are assumed to be rough, but the lubricant is incompressible. It is also clearly demonstrated, in this case that homogenization is an efficient approach. Moreover, several numerical results are presented and compared with those corresponding to where a constant bulk modulus is assumed to govern the lubricant compressibility. In particular, the result shows a significant difference in the asymptotic behavior between the incompressible case and that with constant bulk modulus.
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| 2. |
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| 3. |
- Essel, Emmanuel Kwame, et al.
(författare)
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Homogenization of quasilinear parabolic problems by the method of Rothe and two scale convergence
- 2010
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Ingår i: Applications of Mathematics. - : Institute of Mathematics, Czech Academy of Sciences. - 0862-7940 .- 1572-9109. ; 55:4, s. 305-327
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Tidskriftsartikel (refereegranskat)abstract
- We consider a quasilinear parabolic problem with time dependent coefficients oscillating rapidly in the space variable. The existence and uniqueness results are proved by using Rothe's method combined with the technique of two-scale convergence. Moreover, we derive a concrete homogenization algorithm for giving a unique and computable approximation of the solution.
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| 4. |
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| 5. |
- Oguntuase, James, et al.
(författare)
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Multidimensional Hardy-type inequalities with general kernels
- 2008
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Ingår i: Journal of Mathematical Analysis and Applications. - : Elsevier BV. - 0022-247X .- 1096-0813. ; 348:1, s. 411-418
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Tidskriftsartikel (refereegranskat)abstract
- Some new multidimensional Hardy-type inequalities involving arithmetic mean operators with general positive kernels are derived. Our approach is mainly to use a convexity argument and the results obtained improve some known results in the literature and, in particular, some recent results in [S. Kaijser, L. Nikolova, L.-E. Persson, A. Wedestig, Hardy-type inequalities via convexity, Math. Inequal. Appl. 8 (3) (2005) 403-417] are generalized and complemented.
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| 6. |
- Oguntuase, James, et al.
(författare)
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Refined multidimensional Hardy-type inequalities via superquadracity
- 2008
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Ingår i: Banach Journal of Mathematical Analysis. - : Springer Science and Business Media LLC. - 1735-8787. ; 2:2, s. 129-139
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Tidskriftsartikel (refereegranskat)abstract
- Some new refined multidimensional Hardy-type inequalities for p 2 and their duals are derived and discussed. Moreover, these inequalities hold in the reversed direction when 1 < p 2. The results obtained are based mainly on some new results for superquadratic and subquadratic functions. In particular, our results further extend the recent results in [J.A. Oguntuase and L.-E. Persson, Refinement of Hardy's inequalities via superquadratic and subquadratic functions, J
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