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Existence of periodic solutions with nonconstant sign in a class of generalized Abel equations
Fractal bodies invisible in 2 and 3 directions
1. | Department of Mathematics, University of Aveiro, Aveiro 3810-193 |
2. | Collaborative Research Network, University of Ballarat, VIC 3353, Australia |
References:
[1] |
A. Aleksenko and A. Plakhov, Bodies of zero resistance and bodies invisible in one direction, Nonlinearity, 22 (2009), 1247-1258.
doi: 10.1088/0951-7715/22/6/001. |
[2] |
P. Bachurin, K. Khanin, J. Marklof and A. Plakhov, Perfect retroreflectors and billiard dynamics, J. Modern Dynam., 5 (2011), 33-48. |
[3] |
D. Bucur and G. Buttazzo, "Variational Methods in Shape Optimization Problems," Birkhäuser (2005). |
[4] |
G. Buttazzo and B. Kawohl, On Newton's problem of minimal resistance, Math. Intell., 15 (1993), 7-12.
doi: 10.1007/BF03024318. |
[5] |
M. Comte and T. Lachand-Robert, Newton's problem of the body of minimal resistance under a single-impact assumption, Calc. Var. Partial Differ. Equ., 12 (2001), 173-211.
doi: 10.1007/PL00009911. |
[6] |
T. Lachand-Robert and E. Oudet, Minimizing within convex bodies using a convex hull method, SIAM J. Optim., 16 (2006), 368-379.
doi: 10.1137/040608039. |
[7] |
T. Lachand-Robert and M. A. Peletier, Newton's problem of the body of minimal resistance in the class of convex developable functions, Math. Nachr., 226 (2001), 153-176.
doi: 10.1002/1522-2616(200106)226:1<153::AID-MANA153>3.3.CO;2-U. |
[8] |
I. Newton, Philosophiae naturalis principia mathematica, (1687). |
[9] |
A. Plakhov, Scattering in billiards and problems of Newtonian aerodynamics, Russ. Math. Surv., 64 (2009), 873-938.
doi: 10.1070/RM2009v064n05ABEH004642. |
[10] |
A. Plakhov, Mathematical retroreflectors, Discr. Contin. Dynam. Syst.-A, 30 (2011), 1211-1235.
doi: 10.3934/dcds.2011.30.1211. |
[11] |
A. Plakhov and A. Aleksenko, The problem of the body of revolution of minimal resistance, ESAIM Control Optim. Calc. Var. 16 (2010), 206-220. |
[12] |
A. Plakhov and V. Roshchina, Invisibility in billiards, Nonlinearity, 24 (2011), 847-854.
doi: 10.1088/0951-7715/24/3/007. |
[13] |
, "Invisibility,'' Wikipedia article. Available from: http://en.wikipedia.org/wiki/Invisibility. |
[14] |
, "Unsichtbarkeit,'' Wikipedia article. Available from: http://de.wikipedia.org/wiki/Unsichtbarkeit. |
show all references
References:
[1] |
A. Aleksenko and A. Plakhov, Bodies of zero resistance and bodies invisible in one direction, Nonlinearity, 22 (2009), 1247-1258.
doi: 10.1088/0951-7715/22/6/001. |
[2] |
P. Bachurin, K. Khanin, J. Marklof and A. Plakhov, Perfect retroreflectors and billiard dynamics, J. Modern Dynam., 5 (2011), 33-48. |
[3] |
D. Bucur and G. Buttazzo, "Variational Methods in Shape Optimization Problems," Birkhäuser (2005). |
[4] |
G. Buttazzo and B. Kawohl, On Newton's problem of minimal resistance, Math. Intell., 15 (1993), 7-12.
doi: 10.1007/BF03024318. |
[5] |
M. Comte and T. Lachand-Robert, Newton's problem of the body of minimal resistance under a single-impact assumption, Calc. Var. Partial Differ. Equ., 12 (2001), 173-211.
doi: 10.1007/PL00009911. |
[6] |
T. Lachand-Robert and E. Oudet, Minimizing within convex bodies using a convex hull method, SIAM J. Optim., 16 (2006), 368-379.
doi: 10.1137/040608039. |
[7] |
T. Lachand-Robert and M. A. Peletier, Newton's problem of the body of minimal resistance in the class of convex developable functions, Math. Nachr., 226 (2001), 153-176.
doi: 10.1002/1522-2616(200106)226:1<153::AID-MANA153>3.3.CO;2-U. |
[8] |
I. Newton, Philosophiae naturalis principia mathematica, (1687). |
[9] |
A. Plakhov, Scattering in billiards and problems of Newtonian aerodynamics, Russ. Math. Surv., 64 (2009), 873-938.
doi: 10.1070/RM2009v064n05ABEH004642. |
[10] |
A. Plakhov, Mathematical retroreflectors, Discr. Contin. Dynam. Syst.-A, 30 (2011), 1211-1235.
doi: 10.3934/dcds.2011.30.1211. |
[11] |
A. Plakhov and A. Aleksenko, The problem of the body of revolution of minimal resistance, ESAIM Control Optim. Calc. Var. 16 (2010), 206-220. |
[12] |
A. Plakhov and V. Roshchina, Invisibility in billiards, Nonlinearity, 24 (2011), 847-854.
doi: 10.1088/0951-7715/24/3/007. |
[13] |
, "Invisibility,'' Wikipedia article. Available from: http://en.wikipedia.org/wiki/Invisibility. |
[14] |
, "Unsichtbarkeit,'' Wikipedia article. Available from: http://de.wikipedia.org/wiki/Unsichtbarkeit. |
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