Geodesic
Shape optimization problems for 3-dimensional bodies, moving in a planet atmosphere
The Bulletin of Irkutsk State University. Series Mathematics, Tome 4 (2011) no. 3, pp. 20-31 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper presents the statements and analytical solutions of optimization problems of finding optimal 3-dimensional body shapes from viewpoint of minimum of radiation heat transfer. In a class of slender bodies possessing homotetic property the initial optimization problem may be reduced to two separated problems of finding optimal longitudinal and transverse contours. From mathematical point of view these problems are variational ones with a glance to various isoperimetric and boundary conditions. The investigation of the problem of determining the optimal transversal contour has shown that there exists a class of variational solutions composed of $n$ identical cycles.
Keywords: variational problems, optimal aerodynamic design, radiation heat transfer. 
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M. A. Arguchintseva. Shape optimization problems for 3-dimensional bodies, moving in a planet atmosphere. The Bulletin of Irkutsk State University. Series Mathematics, Tome 4 (2011) no. 3, pp. 20-31. http://geodesic.mathdoc.fr/item/IIGUM_2011_4_3_a1/

[1] M. A. Arguchintseva, N. N. Pilyugin, “Prostranstvennye formy tel s minimalnym nagrevom poverkhnosti pri giperzvukovom dvizhenii v atmosfere”, Kosm. issledovaniya, 30:5 (1992), 615–628

[2] M. A. Arguchintseva, “Analiticheskoe reshenie odnogo klassa variatsionnykh zadach aerodinamiki bolshikh skorostei”, Izv. Irkut. gos. un-ta. Ser. Matematika, 1:1 (2007), 52–61

[3] M. A. Arguchintseva, N. N. Pilyugin, Ekstremalnye zadachi radiatsionnoi gazovoi dinamiki, Izd-vo Mosk. un-ta, M., 1997, 197 pp.

[4] S. A. Losev, N. N. Pilyugin, S. T. Surzhikov, Modelirovanie radiatsionnykh protsessov v mekhanike sploshnoi sredy, Izd-vo MGU, M., 1990, 184 pp.

[5] N. A. Ostapenko, G. E. Yakunina, “O forme tonkikh prostranstvennykh tel s maksimalnoi glubinoi pronikaniya v plotnye sredy”, Priklad. matematika i mekhanika, 63:6 (1999), 1018–1034 | MR | Zbl

[6] A. I. Shvets, Aerodinamika sverkhzvukovykh form, Izd-vo Mosk. un-ta, M., 1987, 208 pp.

[7] A. Miele (red.), Teoriya optimalnykh aerodinamicheskikh form, Mir, M., 1969, 507 pp.