Cimatti, Giovanni Existence and uniqueness for nonlinear Reynolds equations. (English) Zbl 0624.76090 Int. J. Eng. Sci. 24, 827-834 (1986). The pressure distribution in a gas-lubricated bearing is given by the nonlinear Reynolds equation with the boundary value problem \(\nabla \cdot (H^ 3P\nabla P)=\Lambda (HP)_ x\) in \(\Omega\), \(P=G\) on \(\partial \Omega\). Various results of existence and uniqueness for this equation are presented. Furthermore the system of nonlinear equations arising when elastic deformation of the bearing surfaces is not neglected is discussed. Cited in 6 Documents MSC: 76N20 Boundary-layer theory for compressible fluids and gas dynamics 76N15 Gas dynamics, general 35Q99 Partial differential equations of mathematical physics and other areas of application Keywords:a priori bound; pressure distribution; gas-lubricated bearing; nonlinear Reynolds equation; boundary value problem; existence; uniqueness; elastic deformation PDF BibTeX XML Cite \textit{G. Cimatti}, Int. J. Eng. Sci. 24, 827--834 (1986; Zbl 0624.76090) Full Text: DOI References: [1] Adams, R.A., Sobolev spaces, (1975), Academic Press New York · Zbl 0186.19101 [2] Berger, M.S., Nonlinearity and functional analysis, (1977), Academic Press New York [3] Cesari, L., Optimization theory and application, (1983), Springer-Verlag New York [4] Chandra, J.C.; Davis, P.W., Arch. rat. mech. anal., 54, 257, (1974) [5] G. CIMATTI, Appl. Math. Opt., in press. [6] Cimatti, G., Appl. math. opt., 3, 227, (1977) [7] Friedman, A., Variational principles and free-boundary problems, (1982), John Wiley & Sons New York · Zbl 0564.49002 [8] Gilbarg, D.; Trudinger, N.S., Elliptic partial differential equations of the second order, (1983), Springer-Verlag New York · Zbl 0691.35001 [9] Kinderlehrer, D.; Stampacchia, G., An introduction to variational inequalities and their applications, (1980), Academic Press New York · Zbl 0457.35001 [10] Pinkus, O.; Sternlicht, B., Theory of hydrodynamic lubrication, (1961), McGraw-Hill London · Zbl 0100.23001 [11] Stampacchia, G., Equations elliptiques du second ordre a coefficients discontinus, () · Zbl 0151.15501 [12] Steinmetz, W.J., SIAM J. appl. math., 26, 816, (1974) [13] M. CHIPOT and M. LUSKIN, to appear. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.