We characterize the solution to the Newton minimal resistance problem in a class of radial q-concave profiles. We also give the corresponding result for one-dimensional profiles. Moreover, we provide a numerical optimization algorithm for the general nonradial case.
Accepté le :
DOI : 10.1051/cocv/2018016
Mots-clés : Newton minimal resistance problem, shape optimization
@article{COCV_2019__25__A27_0,
author = {Mainini, Edoardo and Monteverde, Manuel and Oudet, Edouard and Percivale, Danilo},
title = {The minimal resistance problem in a class of non convex bodies},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {25},
year = {2019},
doi = {10.1051/cocv/2018016},
zbl = {1439.49078},
mrnumber = {3989206},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2018016/}
}
TY - JOUR AU - Mainini, Edoardo AU - Monteverde, Manuel AU - Oudet, Edouard AU - Percivale, Danilo TI - The minimal resistance problem in a class of non convex bodies JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2019 VL - 25 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2018016/ DO - 10.1051/cocv/2018016 LA - en ID - COCV_2019__25__A27_0 ER -
%0 Journal Article %A Mainini, Edoardo %A Monteverde, Manuel %A Oudet, Edouard %A Percivale, Danilo %T The minimal resistance problem in a class of non convex bodies %J ESAIM: Control, Optimisation and Calculus of Variations %D 2019 %V 25 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2018016/ %R 10.1051/cocv/2018016 %G en %F COCV_2019__25__A27_0
Mainini, Edoardo; Monteverde, Manuel; Oudet, Edouard; Percivale, Danilo. The minimal resistance problem in a class of non convex bodies. ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 27. doi : 10.1051/cocv/2018016. http://www.numdam.org/articles/10.1051/cocv/2018016/
[1] BlackBoxOptim.jl, A global optimization framework for Julia. Available at: https://github.com/robertfeldt/BlackBoxOptim.jl. (2019)
[2] , and , A symmetry problem in the calculus of variations. Calc. Var. Partial Diff. Equ. 4 (1996) 593–599. | DOI | MR | Zbl
[3] , A survey on the Newton problem of optimal profiles, in Variational Analysis and Aerospace Engineering. Vol. 33 of Optimization and Its Applications. Springer (2009) 33–48. | MR | Zbl
[4] and , Shape optimization problems over classes of convex domains. J. Convex Anal. 4 (1997) 343–351. | MR | Zbl
[5] and , On Newton’s problem of minimal resistance. Math. Intell. 15 (1993) 7–12. | DOI | MR | Zbl
[6] , and , Minimum problems over sets of concave functions and related questions. Math. Nachr. 173 (1995) 71–89. | DOI | MR | Zbl
[7] and , Newton’s problem of the body of minimal resistance under a single-impact assumption. Calc. Var. Partial Diff. Equ. 12 (2001) 173–211. | DOI | MR | Zbl
[8] and , Existence of minimizers for the Newton’s problem of the body of minimal resistance under a single-impact assumption. J. Anal. Math. 83 (2001) 313–335. | DOI | MR | Zbl
[9] , A History of the Calculus of Variations from the 17th Through the 19th Century. Springer-Verlag, Heidelberg (1980). | MR | Zbl
[10] and , Minimizing within convex bodies using a convex hull method. SIAM J. Optim. 16 (2005) 368–379. | DOI | MR | Zbl
[11] and , Newton’s problem of the body of minimal resistance in the class of convex developable functions. Math. Nachr. 226 (2001) 153–176. | DOI | MR | Zbl
[12] , , and , Newton’s aerodynamic for non convex bodies. Rend. Lincei Mat. Appl. 28 (2017) 885–896. | MR | Zbl
[13] , Nonconvex integrals of the calculus of variations, in Methods of Nonconvex Analysis (Varenna, 1989). Vol. 1446 of Lecture Notes in Mathematics. Springer-Verlag, Berlin (1990) 16–57. | DOI | MR | Zbl
[14] , The problem of minimal resistance for functions and domains. SIAM J. Math. Anal. 46 (2014) 2730–2742. | DOI | MR | Zbl
[15] , Newton’s problem of minimal resistance under the single impact assumption. Nonlinearity 29 (2016) 465–488. | DOI | MR | Zbl
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