The topological asymptotic for the Navier-Stokes equations

 Access to full text

 Full (PDF)

1. [1] G. Allaire, Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes. I. Abstract framework, a volume distribution of holes. Arch. Rational Mech. Anal. 113 (1990) 209–259. Zbl0724.76020
2. [2] G. Allaire, Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes. II. Noncritical sizes of the holes for a volume distribution and a surface distribution of holes. Arch. Rational Mech. Anal. 113 (1990) 261–298. Zbl0724.76021
3. [3] G. Allaire, Shape optimization by the homogenization method. Springer, Appl. Math. Sci. 146 (2002). Zbl0990.35001MR1859696
4. [4] S. Amstutz, The topological asymptotic for the Helmholtz equation: insertion of a hole, a crack and a dielectric object. Rapport MIP No. 03–05 (2003). 
5. [5] M. Bendsoe, Optimal topology design of continuum structure: an introduction. Technical report, Departement of mathematics, Technical University of Denmark, DK2800 Lyngby, Denmark (1996). 
6. [6] R. Dautray and J.-L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques. Masson, collection CEA 6 (1987). Zbl0642.35001MR918560
7. [7] A. Friedman and M.S. Vogelius, Identification of small inhomogeneities of extreme conductivity byboundary measurements: a theorem of continuous dependence. Arch. Rational Mech. Anal. 105 (1989) 299–326. Zbl0684.35087
8. [8] G. Galdi, An introduction to the mathematical theory of the Navier-Stokes equations. Vols. I and II, Springer-Verlag 39 (1994). Zbl0949.35005MR1284205
9. [9] S. Garreau, Ph. Guillaume and M. Masmoudi, The topological asymptotic for PDE systems: the elasticity case. SIAM J. Control Optim. 39 (2001) 1756–1778. Zbl0990.49028
10. [10] Ph. Guillaume and K. Sid Idris, The topological asymptotic expansion for the Dirichlet problem. SIAM J. Control. Optim. 41 (2002) 1052–1072. Zbl1053.49031
11. [11] Ph. Guillaume and K. Sid Idris, Topological sensitivity and shape optimization for the Stokes equations. Rapport MIP No. 01–24 (2001). Zbl1093.49029
12. [12] M. Hassine and M. Masmoudi, The topological asymptotic expansion for the quasi-Stokes problem. ESAIM: COCV 10 (2004) 478–504. Zbl1072.49027
13. [13] A.M. Il’in, Matching of asymptotic expansions of solutions of boundary value problems. Translations Math. Monographs 102 (1992). Zbl0754.34002
14. [14] J. Jacobsen, N. Olhoff and E. Ronholt, Generalized shape optimization of three-dimensionnal structures using materials with optimum microstructures. Technical report, Institute of Mechanical Engineering, Aalborg University, DK-9920 Aalborg, Denmark (1996). 
15. [15] M. Masmoudi, The Toplogical Asymptotic, Computational Methods for Control Applications, R. Glowinski, H. Kawarada and J. Periaux Eds. GAKUTO Internat. Ser. Math. Sci. Appl. 16 (2001) 53–72. Zbl1082.93584
16. [16] V. Mazya, S. Nazarov and B. Plamenevskij, Asymptotic theory of elliptic boundary value problems in singularly perturbed domains. Birkhäuser Verlag, Oper. Theory Adv. Appl. 101 (2000). Zbl1127.35301
17. [17] S. Nazarov, A. Sequeira and J. Videman, Steady flows of Jeffrey-Hamel type from the half plane into an infinite channel. Linearization on an antisymmetric solution. J. Math. Pures Appl. 80 (2001) 1069–1098. Zbl1042.76013
18. [18] S. Nazarov, A. Sequeira and J. Videman, Steady flows of Jeffrey-Hamel type from the half plane into an infinite channel. Linearization on a symmetric solution. J. Math. Pures Appl. 81 (2001) 781–810. Zbl1043.76015
19. [19] S. Nazarov and M. Specovius-Neugebauer, Approximation of exterior boundary value problems for the Stokes system. Asymptotic Anal. 14 (1997) 223–255. Zbl0884.35130
20. [20] S. Nazarov, M. Specovius-Neugebauer and J. Videman, Nonlinear artificial boundary conditions for the Navier-Stokes equations in an aperture domain. Math. Nachr. 265 (2004) 24–67. Zbl1042.35050
21. [21] B. Samet, S. Amstutz and M. Masmoudi, The topological asymptotic for the Helmholtz equation. SIAM J. Control Optim. 42 (2003) 1523–1544. Zbl1051.49029
22. [22] B. Samet and J. Pommier, The topological asymptotic for the Helmholtz equation with Dirichlet condition on the boundary of an arbitrary shaped hole. SIAM J. Control Optim. 43 (2004) 899–921. Zbl1080.49028
23. [23] A. Schumacher, Topologieoptimisierung von Bauteilstrukturen unter Verwendung von Lopchpositionierungkrieterien. Thesis, Universität-Gesamthochschule-Siegen (1995). 
24. [24] K. Sid Idris, Sensibilité topologique en optimisation de forme. Thèse de l’INSA Toulouse (2001). 
25. [25] J. Sokolowski and A. Zochowski, On the topological derivative in shape optimization. SIAM J. Control Optim. 37 (1999) 1241–1272. Zbl0940.49026
26. [26] R. Temam, Navier-Stokes equations. Elsevier (1984). Zbl0568.35002MR769654