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Non-standard dynamics of elastic composites
Homogenization of convection-diffusion equation in infinite cylinder
1. | Narvik University College, Postbox 385, 8505 Narvik, Norway |
2. | Narvik University College, HiN, Postbox 385, 8505 Narvik, Norway, and, P.N. Lebedev Physical Institute RAS, Leninski prospect, 53, Moscow, 117924 |
References:
[1] |
G. Allaire and A. Raphael, Homogenization of a convection-diffusion model with reaction in a porous medium, (English, French summary), C. R. Math. Acad. Sci. Paris, 344 (2007), 523.
|
[2] |
D. G. Aronson and J. Serrin, Local behavior of solutions of quasilinear parabolic equations,, Arch. Rational Mech. Anal., 25 (1967), 81.
doi: 10.1007/BF00281291. |
[3] |
D. G. Aronson, Non-negative solutions of linear parabolic equations,, Ann. Scuola Norm. Sup. Pisa (3), 22 (1968), 607.
|
[4] |
N. S. Bakhvalov and G. P. Panasenko, "Homogenization: Averaging Processes in Periodic Media,", Kluwer, (1989).
|
[5] |
A. Bensoussan, J.-L. Lions and G. Papanicolaou, "Asymptotic Analysis for Periodic Structure,", Studies in Mathematics and its Applications, (1978).
|
[6] |
P. Donato and A. Piatnitski, Averaging of nonstationary parabolic operators with large lower order terms,, Multi Scale Problems and Asymptotic Analysis, 24 (2005), 153.
|
[7] |
M. V. Kozlova and G. P. Panasenko, Averaging a three-dimensional problem of elasticity theory in a nonhomogeneous rod,, Comput. Math. Math. Phys., 31 (1992), 128.
|
[8] |
O. A. Ladyzenskaja, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type,", Translations of Mathematical Monographs, 23 (1967).
|
[9] |
I. Pankratova and A. Piatnitski, On the behaviour at infinity of solutions to stationary convection-diffusion equation in a cylinder,, DCDS-B, 11 (2009), 935.
doi: 10.3934/dcdsb.2009.11.935. |
[10] |
L. Trabucho and J. M. Viaño, Derivation of generalized models for linear elastic beams by asymptotic expansion methods,, Applications of multiple scaling in mechanis (Paris, 4 (1987), 302.
|
[11] |
Z. Tutek, A homogenized model of rod in linear elasticity,, Applications of multiple scaling in mechanis (Paris, 4 (1987), 302.
|
[12] |
V. V. Zhikov, S. M. Kozlov and O. A. Oleinik, "Homogenization of Differential Operators and Integral Functionals,", Springer-Verlag, (1994).
|
[13] |
V. V. Zhikov, On an extension and an application of the two-scale convergence method,, Sb. Math., 191 (2000), 973.
doi: 10.1070/SM2000v191n07ABEH000491. |
show all references
References:
[1] |
G. Allaire and A. Raphael, Homogenization of a convection-diffusion model with reaction in a porous medium, (English, French summary), C. R. Math. Acad. Sci. Paris, 344 (2007), 523.
|
[2] |
D. G. Aronson and J. Serrin, Local behavior of solutions of quasilinear parabolic equations,, Arch. Rational Mech. Anal., 25 (1967), 81.
doi: 10.1007/BF00281291. |
[3] |
D. G. Aronson, Non-negative solutions of linear parabolic equations,, Ann. Scuola Norm. Sup. Pisa (3), 22 (1968), 607.
|
[4] |
N. S. Bakhvalov and G. P. Panasenko, "Homogenization: Averaging Processes in Periodic Media,", Kluwer, (1989).
|
[5] |
A. Bensoussan, J.-L. Lions and G. Papanicolaou, "Asymptotic Analysis for Periodic Structure,", Studies in Mathematics and its Applications, (1978).
|
[6] |
P. Donato and A. Piatnitski, Averaging of nonstationary parabolic operators with large lower order terms,, Multi Scale Problems and Asymptotic Analysis, 24 (2005), 153.
|
[7] |
M. V. Kozlova and G. P. Panasenko, Averaging a three-dimensional problem of elasticity theory in a nonhomogeneous rod,, Comput. Math. Math. Phys., 31 (1992), 128.
|
[8] |
O. A. Ladyzenskaja, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type,", Translations of Mathematical Monographs, 23 (1967).
|
[9] |
I. Pankratova and A. Piatnitski, On the behaviour at infinity of solutions to stationary convection-diffusion equation in a cylinder,, DCDS-B, 11 (2009), 935.
doi: 10.3934/dcdsb.2009.11.935. |
[10] |
L. Trabucho and J. M. Viaño, Derivation of generalized models for linear elastic beams by asymptotic expansion methods,, Applications of multiple scaling in mechanis (Paris, 4 (1987), 302.
|
[11] |
Z. Tutek, A homogenized model of rod in linear elasticity,, Applications of multiple scaling in mechanis (Paris, 4 (1987), 302.
|
[12] |
V. V. Zhikov, S. M. Kozlov and O. A. Oleinik, "Homogenization of Differential Operators and Integral Functionals,", Springer-Verlag, (1994).
|
[13] |
V. V. Zhikov, On an extension and an application of the two-scale convergence method,, Sb. Math., 191 (2000), 973.
doi: 10.1070/SM2000v191n07ABEH000491. |
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