An inverse problem for the compressible Reynolds equation
Authors:
Rene Dager, Mihaela Negreanu and J. Ignacio Tello
Journal:
Quart. Appl. Math. 73 (2015), 607-614
MSC (2010):
Primary 35Q35, 35R30, 47H11
DOI:
https://doi.org/10.1090/qam/1398
Published electronically:
September 10, 2015
MathSciNet review:
3432274
Full-text PDF Free Access
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Additional Information
Abstract: We study the existence of solutions to a system of equations for equilibrium positions in lubricated journal bearings under load effects. The mechanism under consideration consists of two parallel cylinders, one inside the other, in close distance and relative motion. The unknowns of the problem are the equilibrium position of the inner cylinder and the pressure of the lubricant described by the compressible Reynolds equation. To complete the system, Newton’s second law gives the equilibrium of forces. We present results on existence of solutions for a range of applied forces $F$.
References
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- Ionel Ciuperca and J. Ignacio Tello, Lack of contact in a lubricated system, Quart. Appl. Math. 69 (2011), no. 2, 357–378. MR 2729893, DOI https://doi.org/10.1090/S0033-569X-2011-01235-1
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- E. H. Rothe, Introduction to various aspects of degree theory in Banach spaces, Mathematical Surveys and Monographs, vol. 23, American Mathematical Society, Providence, RI, 1986. MR 852987
References
- G. Bayada and C. Vázquez, A survey on mathematical aspects of lubrication problems, Boletín de la Sociedad Española de Matemática Aplicada 39 (2007), 37–74. MR 2406973 (2009d:76042)
- R. K. Brunner, J. M. Harker, K. E. Haughton, and A. G. Osterlund, A gas film lubrication study. III. Experimental investigation of pivoted slider bearings, IBM J. Res. Develop. 3 (1959), 260–274. MR 0105950 (21 \#4684)
- A. Burgdorfer, The influence of the molecular mean free path on the performance of hydrodynamics gas lubricated bearings, J. Basic Eng. Trans. ASME 81 (1956), 94–100.
- G. Buscaglia, I. Ciuperca, and M. Jai, Existence and uniqueness for several non-linear elliptic problems arising in lubrication theory, J. Differential Equations 218 (2005), no. 1, 187–215. MR 2174972 (2006k:35080), DOI https://doi.org/10.1016/j.jde.2005.06.018
- I. Ciuperca, M. Jai, and J. I. Tello, On the existence of solutions of equilibria in lubricated journal bearings, SIAM J. Math. Anal. 40 (2009), no. 6, 2316–2327. MR 2481296 (2010i:35434), DOI https://doi.org/10.1137/080724228
- Ionel Ciuperca and J. Ignacio Tello, Lack of contact in a lubricated system, Quart. Appl. Math. 69 (2011), no. 2, 357–378. MR 2729893 (2012g:76057)
- J. Durany, G. García, and C. Vázquez, Numerical simulation of a lubricated Hertzian contact problem under imposed load, Finite Elem. Anal. Des. 38 (2002), no. 7, 645–658. MR 1897446 (2003c:74093), DOI https://doi.org/10.1016/S0168-874X%2801%2900097-X
- S. Fukui and R. Kaneko, Analysis of ultra-thin gas film lubrication based on linearized Boltzmann equation: first report-derivation of a generalized lubrication equation including thermal creep flow, ASME J. Tribol. 110 (1988), 253–262.
- I. Hafidi, An investigation of the singular perturbation problems for the compressible Reynolds equation, Differential Integral Equations 22 (2009), no. 1-2, 177–200. MR 2483018 (2010e:35066)
- E. H. Rothe, Introduction to various aspects of degree theory in Banach spaces, Mathematical Surveys and Monographs, vol. 23, American Mathematical Society, Providence, RI, 1986. MR 852987 (87m:47145)
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Additional Information
Rene Dager
Affiliation:
Depto. de Matemática Aplicada, Universidad Politécnica de Madrid, 28040 Madrid, Spain
ORCID:
0000-0003-3280-2828
Email:
rene.dager@upm.es
Mihaela Negreanu
Affiliation:
Depto. de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain
MR Author ID:
726367
ORCID:
0000-0003-0533-3464
Email:
negreanu@mat.ucm.es
J. Ignacio Tello
Affiliation:
Depto. de Matemática Aplicada a las Tecnologias de la Información y las Comunicaciones, ETSI Sistemas Informáticos, Universidad Politécnica de Madrid, 28031 Madrid, Spain
Email:
j.tello@upm.es
Received by editor(s):
November 1, 2013
Published electronically:
September 10, 2015
Additional Notes:
The first author’s work was partly supported by project MTM2013-42907-P, Ministry of Economy, Spain
Article copyright:
© Copyright 2015
Brown University
