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About interface conditions for coupling hydrostatic and nonhydrostatic Navier-Stokes flows
Homogenization: In mathematics or physics?
1. | Department of Mathematics, Soochow University, Suzhou 215006, China |
2. | High Speed Aerodynamics Institute, China Aerodynamisc Development and Research Center, Mianyang 622661, China |
References:
[1] |
G. Allaire, Homogenization et convergence a deux echelles, application a un probleme de convection diffusion. C.R.Acad. Sci. Paris, 312 (1991), 581-586. |
[2] |
G. Allaire, Homogenization and two-scale convergence, SIAM J. Math. Anal., 23 (1992), 1482-1518.
doi: 10.1137/0523084. |
[3] |
I. Babuška, Solution of problem with interfaces and singularities, in Mathematical aspects of finite elements in partial differential equations, C. de Boor ed., Academic Press, New York, (1974), 213-277. |
[4] |
I. Babuška, Homogenization approach in engineering, Lecture notes in economics and mathematical systems, M. Beckman and H. P. Kunzi(eds.), Springer-Verlag, 134 (1976), 137-153. |
[5] |
I. Babuška, Homogenization and its application. Mathematical and computational problems, Numerical solution of partial differential equations, III, Academic Press, (1976), 89-116. |
[6] |
I. Babuška, The computational aspects of the homogenization problem, Computing methods in applied sciences and engineering, I, Lecture notes in mathematics, Springer-Verlag,Berlin Heidelberg New York, 704 (1976), 309-316. |
[7] |
A. Bensousan, J. L. Lions and G. Papanicolaou, Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam, 1978. |
[8] |
D. Cioranescu and P. Donato, An Introduction to Homogenization, Oxford Lecture Series in Mathematics and Its Applications, 17, Oxford university press, 1999. |
[9] |
S. M. Kozlov, The averaging of random operators, Mat.Sb.(N.S), 109 (1979), 188-202,327. |
[10] |
K. Lichtenecker, Die dielektrizitätskonstante natürlicher und künstlicher mischkörper, Phys. Zeitschr., XXVII (1926), 115-158. |
[11] |
J. C. Maxwell, A Treatise on Electricity and Magnetism, 3rd Ed. , Clarendon Press, Oxford, 1881. |
[12] |
F. Murat and L. Tartar, H-convergence, Topics in the Mathematical Modelling of Composite Materials, 31 (1997), 21-43.
doi: 10.1007/978-1-4612-2032-9_3. |
[13] |
G. Nguestseng, A general convergence result for a functional related to the theory of homogenization, SIAM J. Math. Anal., 20 (1989), 608-623.
doi: 10.1137/0520043. |
[14] |
O. A. Olenik and A. S. Shamaev and G. A. Yosifian, Mathematical Problems in Elasticity and Homogenization, Studies in mathematics and its applications, J.L. Lions, G.Papanicolaou, H. Fujita, H.B. Keller, 26, North-Holland, 1992. |
[15] |
S. Poisson, Second mémoire sur la théorie du magnétisme, Mem. Acad. France 5, 1822. |
[16] |
S. Spagnolo, Sul limite delle soluzioni di problemi di Cauchy relativi all' equatione del calore, Ann. Scuola Norm. Sup. Pisa, 21 (1967), 657-699. |
[17] |
T. A. Suslina, Homogenization of a stationary periodic maxwell system, St. Petersburg Math. J., 16 (2005), 863-922.
doi: 10.1090/S1061-0022-05-00883-6. |
[18] |
L. Tartar, Compensated compactness and partial differential equations, in Nolinear Analysis and Mechanics: Heriot-Watt Symposium, Pitman, 39 (1979), 136-212. |
[19] |
L. Tartar, H-measure, a new approach for studying homogenization, oscillations and concentration effects in partial differential equations, Proc. Roy. Soc. Edinburgh, 115 (1990), 193-230.
doi: 10.1017/S0308210500020606. |
[20] |
T. Yu and X. Yue, Residual-free bubble methods for numerical homogenization of elliptic problems, Commun. Math. Sci., 9 (2011), 1163-1176.
doi: 10.4310/CMS.2011.v9.n4.a12. |
[21] |
V. V. Zhikov, Some estimates from homogenization theory, (Russian) Dokl. Akad. Nauk, 406 (2006), 597-601. |
[22] |
V. V. Zhikov and O. A. Oleinik, Homogenization and G-convergence of differential operators, Russ. Math. Surv., 34 (1979), 65-147. |
[23] |
V. V. Zhikov, S. M. Kozlov and O. A. Oleinik, Homogenization of Differential Operators and Integral Functionals, Springer Berlin, 1994.
doi: 10.1007/978-3-642-84659-5. |
show all references
References:
[1] |
G. Allaire, Homogenization et convergence a deux echelles, application a un probleme de convection diffusion. C.R.Acad. Sci. Paris, 312 (1991), 581-586. |
[2] |
G. Allaire, Homogenization and two-scale convergence, SIAM J. Math. Anal., 23 (1992), 1482-1518.
doi: 10.1137/0523084. |
[3] |
I. Babuška, Solution of problem with interfaces and singularities, in Mathematical aspects of finite elements in partial differential equations, C. de Boor ed., Academic Press, New York, (1974), 213-277. |
[4] |
I. Babuška, Homogenization approach in engineering, Lecture notes in economics and mathematical systems, M. Beckman and H. P. Kunzi(eds.), Springer-Verlag, 134 (1976), 137-153. |
[5] |
I. Babuška, Homogenization and its application. Mathematical and computational problems, Numerical solution of partial differential equations, III, Academic Press, (1976), 89-116. |
[6] |
I. Babuška, The computational aspects of the homogenization problem, Computing methods in applied sciences and engineering, I, Lecture notes in mathematics, Springer-Verlag,Berlin Heidelberg New York, 704 (1976), 309-316. |
[7] |
A. Bensousan, J. L. Lions and G. Papanicolaou, Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam, 1978. |
[8] |
D. Cioranescu and P. Donato, An Introduction to Homogenization, Oxford Lecture Series in Mathematics and Its Applications, 17, Oxford university press, 1999. |
[9] |
S. M. Kozlov, The averaging of random operators, Mat.Sb.(N.S), 109 (1979), 188-202,327. |
[10] |
K. Lichtenecker, Die dielektrizitätskonstante natürlicher und künstlicher mischkörper, Phys. Zeitschr., XXVII (1926), 115-158. |
[11] |
J. C. Maxwell, A Treatise on Electricity and Magnetism, 3rd Ed. , Clarendon Press, Oxford, 1881. |
[12] |
F. Murat and L. Tartar, H-convergence, Topics in the Mathematical Modelling of Composite Materials, 31 (1997), 21-43.
doi: 10.1007/978-1-4612-2032-9_3. |
[13] |
G. Nguestseng, A general convergence result for a functional related to the theory of homogenization, SIAM J. Math. Anal., 20 (1989), 608-623.
doi: 10.1137/0520043. |
[14] |
O. A. Olenik and A. S. Shamaev and G. A. Yosifian, Mathematical Problems in Elasticity and Homogenization, Studies in mathematics and its applications, J.L. Lions, G.Papanicolaou, H. Fujita, H.B. Keller, 26, North-Holland, 1992. |
[15] |
S. Poisson, Second mémoire sur la théorie du magnétisme, Mem. Acad. France 5, 1822. |
[16] |
S. Spagnolo, Sul limite delle soluzioni di problemi di Cauchy relativi all' equatione del calore, Ann. Scuola Norm. Sup. Pisa, 21 (1967), 657-699. |
[17] |
T. A. Suslina, Homogenization of a stationary periodic maxwell system, St. Petersburg Math. J., 16 (2005), 863-922.
doi: 10.1090/S1061-0022-05-00883-6. |
[18] |
L. Tartar, Compensated compactness and partial differential equations, in Nolinear Analysis and Mechanics: Heriot-Watt Symposium, Pitman, 39 (1979), 136-212. |
[19] |
L. Tartar, H-measure, a new approach for studying homogenization, oscillations and concentration effects in partial differential equations, Proc. Roy. Soc. Edinburgh, 115 (1990), 193-230.
doi: 10.1017/S0308210500020606. |
[20] |
T. Yu and X. Yue, Residual-free bubble methods for numerical homogenization of elliptic problems, Commun. Math. Sci., 9 (2011), 1163-1176.
doi: 10.4310/CMS.2011.v9.n4.a12. |
[21] |
V. V. Zhikov, Some estimates from homogenization theory, (Russian) Dokl. Akad. Nauk, 406 (2006), 597-601. |
[22] |
V. V. Zhikov and O. A. Oleinik, Homogenization and G-convergence of differential operators, Russ. Math. Surv., 34 (1979), 65-147. |
[23] |
V. V. Zhikov, S. M. Kozlov and O. A. Oleinik, Homogenization of Differential Operators and Integral Functionals, Springer Berlin, 1994.
doi: 10.1007/978-3-642-84659-5. |
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