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On the asymptotic behavior of variational inequalities set in cylinders
1. | Institute of Mathematics, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich |
2. | Technische Universität Darmstadt, Department of Mathematics, Schlossgartenstr. 7, D-64289 Darmstadt, Germany |
References:
[1] |
B. Brighi and S. Guesmia, On elliptic boundary value problems of order 2m in cylindrical domain of large size, Adv. Math. Sci. Appl., 18 (2008), 237-250. |
[2] |
M. Chipot, "l goes to plus infinity," Birkhäuser, 2002.
doi: 10.1007/978-3-0348-8173-9. |
[3] |
M. Chipot and S. Mardare, Asymptotic behaviour of the Stokes problem in cylinders becoming unbounded in one direction, J. Math. Pures Appl. (9), 90 (2008), 133-159.
doi: 10.1016/j.matpur.2008.04.002. |
[4] |
M. Chipot and A. Rougirel, On the asymptotic behaviour of the solution of elliptic problems in cylindrical domains becoming unbounded, Commun. Contemp. Math., 4 (2002), 15-44.
doi: 10.1142/S0219199702000555. |
[5] |
M. Chipot and A. Rougirel, On the asymptotic behaviour of the eigenmodes for elliptic problems in domains becoming unbounded, Trans. Amer. Math. Soc., 360 (2008), 3579-3602.
doi: 10.1090/S0002-9947-08-04361-4. |
[6] |
M. Chipot and Y. Xie, On the asymptotic behaviour of elliptic problems with periodic data, C. R. Math. Acad. Sci. Paris, 339 (2004), 477-482.
doi: 10.1016/j.crma.2004.09.007. |
[7] |
M. Chipot and Y. Xie, Elliptic problems with periodic data: An asymptotic analysis, J. Math. Pures Appl. (9), 85 (2006), 345-370.
doi: 10.1016/j.matpur.2005.07.002. |
[8] |
M. Chipot and K. Yeressian, Exponential rates of convergence by an iteration technique, C. R. Math. Acad. Sci. Paris, 346 (2008), 21-26.
doi: 10.1016/j.crma.2007.12.004. |
[9] |
C. O. Horgan and J. K. Knowles, Recent developments concerning Saint-Venant's principle, Adv. in Appl. Mech., 23 (1983), 179-269.
doi: 10.1016/S0065-2156(08)70244-8. |
[10] |
C. O. Horgan and L. E. Payne, Decay estimates for second-order quasilinear partial differential equations, Adv. in Appl. Math., 5 (1984), 309-332.
doi: 10.1016/0196-8858(84)90012-5. |
[11] |
C. O. Horgan and L. T. Wheeler, Spatial decay estimates for the Navier-Stokes equations with application to the problem of entry flow, SIAM J. Appl. Math., 35 (1978), 97-116.
doi: 10.1137/0135008. |
[12] |
D. Kinderlehrer and G. Stampacchia, "An Introduction to Variational Inequalities and Their Applications," Academic Press, 1980. |
[13] |
J. K. Knowles, On Saint-Venant's principle in the two-dimensional linear theory of elasticity, Arch. Rational Mech. Anal., 21 (1966), 1-22. |
[14] |
J. L. Lions and G. Stampacchia, Variational inequalities, Comm. Pure Appl. Math., 20 (1967), 493-519.
doi: 10.1002/cpa.3160200302. |
[15] |
O. A. Oleinik and G. A. Yosifian, Boundary value problems for second order elliptic equations in unbounded domains and Saint-Venant's principle, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 4 (1977), 269-290. |
[16] | |
[17] |
R. A. Toupin, Saint-Venant's principle, Arch. Rational Mech. Anal., 18 (1965), 83-96. |
[18] |
K. Yeressian, "Spatial Asymptotic Behaviour of Elliptic Equations and Variational Inequalities," Ph.D thesis, University of Zurich, 2010. |
show all references
References:
[1] |
B. Brighi and S. Guesmia, On elliptic boundary value problems of order 2m in cylindrical domain of large size, Adv. Math. Sci. Appl., 18 (2008), 237-250. |
[2] |
M. Chipot, "l goes to plus infinity," Birkhäuser, 2002.
doi: 10.1007/978-3-0348-8173-9. |
[3] |
M. Chipot and S. Mardare, Asymptotic behaviour of the Stokes problem in cylinders becoming unbounded in one direction, J. Math. Pures Appl. (9), 90 (2008), 133-159.
doi: 10.1016/j.matpur.2008.04.002. |
[4] |
M. Chipot and A. Rougirel, On the asymptotic behaviour of the solution of elliptic problems in cylindrical domains becoming unbounded, Commun. Contemp. Math., 4 (2002), 15-44.
doi: 10.1142/S0219199702000555. |
[5] |
M. Chipot and A. Rougirel, On the asymptotic behaviour of the eigenmodes for elliptic problems in domains becoming unbounded, Trans. Amer. Math. Soc., 360 (2008), 3579-3602.
doi: 10.1090/S0002-9947-08-04361-4. |
[6] |
M. Chipot and Y. Xie, On the asymptotic behaviour of elliptic problems with periodic data, C. R. Math. Acad. Sci. Paris, 339 (2004), 477-482.
doi: 10.1016/j.crma.2004.09.007. |
[7] |
M. Chipot and Y. Xie, Elliptic problems with periodic data: An asymptotic analysis, J. Math. Pures Appl. (9), 85 (2006), 345-370.
doi: 10.1016/j.matpur.2005.07.002. |
[8] |
M. Chipot and K. Yeressian, Exponential rates of convergence by an iteration technique, C. R. Math. Acad. Sci. Paris, 346 (2008), 21-26.
doi: 10.1016/j.crma.2007.12.004. |
[9] |
C. O. Horgan and J. K. Knowles, Recent developments concerning Saint-Venant's principle, Adv. in Appl. Mech., 23 (1983), 179-269.
doi: 10.1016/S0065-2156(08)70244-8. |
[10] |
C. O. Horgan and L. E. Payne, Decay estimates for second-order quasilinear partial differential equations, Adv. in Appl. Math., 5 (1984), 309-332.
doi: 10.1016/0196-8858(84)90012-5. |
[11] |
C. O. Horgan and L. T. Wheeler, Spatial decay estimates for the Navier-Stokes equations with application to the problem of entry flow, SIAM J. Appl. Math., 35 (1978), 97-116.
doi: 10.1137/0135008. |
[12] |
D. Kinderlehrer and G. Stampacchia, "An Introduction to Variational Inequalities and Their Applications," Academic Press, 1980. |
[13] |
J. K. Knowles, On Saint-Venant's principle in the two-dimensional linear theory of elasticity, Arch. Rational Mech. Anal., 21 (1966), 1-22. |
[14] |
J. L. Lions and G. Stampacchia, Variational inequalities, Comm. Pure Appl. Math., 20 (1967), 493-519.
doi: 10.1002/cpa.3160200302. |
[15] |
O. A. Oleinik and G. A. Yosifian, Boundary value problems for second order elliptic equations in unbounded domains and Saint-Venant's principle, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 4 (1977), 269-290. |
[16] | |
[17] |
R. A. Toupin, Saint-Venant's principle, Arch. Rational Mech. Anal., 18 (1965), 83-96. |
[18] |
K. Yeressian, "Spatial Asymptotic Behaviour of Elliptic Equations and Variational Inequalities," Ph.D thesis, University of Zurich, 2010. |
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