On a non-isothermal, non-Newtonian lubrication problem with Tresca law: Existence and the behavior of weak solutions
Tài liệu tham khảo
Adams, 1975
Amrouche, 1994, Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension, Czechoslovak Math. J., 44, 10.21136/CMJ.1994.128452
Baranger, 1995, Stationary solutions to a quasi-Newtonian flow with viscous heating, Math. Models Methods Appl. Sci., 5, 725, 10.1142/S0218202595000401
Bayada, 2003, On a free boundary problem for Reynolds equation derived from the Stokes system with Tresca boundary conditions, J. Math. Anal. Appl., 282, 212, 10.1016/S0022-247X(03)00140-9
C. Bernardi, T. Chacón Rebollo, R. Lewandowski, F. Murat, A model for two coupled turbulent fluids. I. Analysis of the system, Nonlinear partial differential equations and their applications, Collège de France Seminar, vol. XIV, Paris, 1997/1998, Studies in Mathematical Application, vol. 31, North-Holland, Amsterdam, 2002, pp. 69–102.
Boughanim, 1995, Derivation of the two-dimensional Carreau law for a quasi-Newtonian fluid flow through a thin slab, Appl. Anal., 57, 243, 10.1080/00036819508840351
M. Boukrouche, I. Ciuperca, Asymptotic behaviour of solutions of lubrication problem in a thin domain with a rough boundary and Tresca fluid–solid interface law, Quart. Appl. Math. 64 (2006) 561–591.
Boukrouche, 2004, Asymptotic analysis of a non-Newtonian fluid in a thin domain with Tresca law, Nonlinear Anal. Theory Meth. Appl., 59, 85, 10.1016/S0362-546X(04)00248-2
Boukrouche, 1999, The stationary Stefan problem with convection governed by a non-linear Darcy's law, Math. Methods Appl. Sci., 22, 563, 10.1002/(SICI)1099-1476(19990510)22:7<563::AID-MMA53>3.0.CO;2-O
Boukrouche, 2003, Asymptotic analysis of solutions of a thin film lubrication problem with Coulomb fluid–solid interface law, Int. J. Eng. Sci., 41, 521, 10.1016/S0020-7225(02)00282-3
Boukrouche, 2004, On a lubrication problem with Fourier and Tresca boundary conditions, Math. Models Methods Appl. Sci., 14, 913, 10.1142/S0218202504003490
L. Consiglieri, J. F. Rodrigues, On stationary flows with energy dependent nonlocal viscosities, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 295 (2003);
Kraev. Zadachi Mat. Fiz. i Smezh. Vopr. Teor. Funkts. 33, 99–117, 245–246; translation in J. Math. Sci. (NY) 127(2) (2005) 1875–1885.
Duvaut, 1980, Équilibre d’un solide élastique avec contact unilatéral et frottement de Coulomb, C. R. Acad. Sci. Paris, 290, 263
Duvaut, 1972
Fujita, 1994, A mathematical analysis of motions of viscous incompressible fluid under leak or slip boundary conditions, Math. Fluid Mech. Modeling, Sūrikaisekikenkyūsho Kōkyūroku, 888, 199
Fujita, 2002, Remarks on the Stokes flow under slip and leak boundary conditions of friction type. Topics in mathematical fluid mechanics. Quaderni di Matematica, Dept. Math., Seconda Univ. Napoli, Caserta, 10, 73
Fujita, 2002, A coherent analysis of Stokes flows under boundary conditions of friction type, J. Comput. Appl. Math., 149, 57, 10.1016/S0377-0427(02)00520-4
Fujita, 1998, Variational inequalities for the Stokes equation with boundary conditions of friction type. Recent developments in domain decomposition methods and flow problems, GAKUTO Int. Ser. Math. Sci. Appl., 11, 15
Gallouët, 1994, Existence of a solution to a coupled elliptic system, Appl. Math. Lett., 7, 49, 10.1016/0893-9659(94)90030-2
Gallouët, 2003, On a turbulent system with unbounded eddy viscosities, Nonlinear Anal., 52, 1051, 10.1016/S0362-546X(01)00890-2
R.P. Gilbert, M. Fang, Nonlinear systems arising from nonisothermal, non-Newtonian Hele-Shaw flows in the presence of body forces and sources, Math. Comput. Modelling 2002.
Gilbert, 1996, Nonisothermal, Non-Newtonian Hele-Shaw flows, II. Asymptotics and existence of weak solutions, Nonlinear Anal., 27, 539, 10.1016/0362-546X(95)00022-N
Jacobson, 1997, At the boundary between lubrication and wear, 291
Jacobson, 1984, Non-Newtonian fluid model incorporated into elastohydrodynamic lubrication of rectangular contacts, J. Tribol., 106, 275, 10.1115/1.3260901
Mikelić, 1995, Mathematical derivation of the power law describing polymer flow through a thin slab, RAIRO Modél. Math. Anal. Numér., 29, 3, 10.1051/m2an/1995290100031
Morrey, 1966
P.P. Mosolov, V.P. Mjasnikov, A proof of Korn's inequality, Dokl. Akad. Nauk SSSR 201 (1971) 36–39 (in Russian).
Oden, 1986
R. Pit, Mesure locale de la vitesse à l’interface solide–liquide simple: Glissement et rôle des interactions, Thèse Physique Université Paris XI, 1999.
R. Pit, H. Hervet, L. Léger, Direct experimental evidences for flow with slip at hexadecane solid interfaces, La revue de Métallurgie-CIT/Science, February 2001.
Serrin, 1959, Mathematical principles of classical fluid mechanics, Handb. Phys., 8, 125
Shieh, 1991, Film collapse in EHL and micro-EHL, J. Tribol., 113, 372, 10.1115/1.2920631
J.L. Tevaarwerk, The shear of hydrodynamic oil films, Ph.D. Thesis, Cambridge, England, 1976.
