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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 |
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A. Aleksenko and A. Plakhov, Bodies of zero resistance and bodies invisible in one direction,, Nonlinearity, 22 (2009), 1247.
doi: 10.1088/0951-7715/22/6/001. |
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P. Bachurin, K. Khanin, J. Marklof and A. Plakhov, Perfect retroreflectors and billiard dynamics,, J. Modern Dynam., 5 (2011), 33.
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D. Bucur and G. Buttazzo, "Variational Methods in Shape Optimization Problems,", Birkhäuser (2005)., (2005).
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G. Buttazzo and B. Kawohl, On Newton's problem of minimal resistance,, Math. Intell., 15 (1993), 7.
doi: 10.1007/BF03024318. |
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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.
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.
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.
doi: 10.1002/1522-2616(200106)226:1<153::AID-MANA153>3.3.CO;2-U. |
[8] |
I. Newton, Philosophiae naturalis principia mathematica,, (1687)., (1687). Google Scholar |
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A. Plakhov, Scattering in billiards and problems of Newtonian aerodynamics,, Russ. Math. Surv., 64 (2009), 873.
doi: 10.1070/RM2009v064n05ABEH004642. |
[10] |
A. Plakhov, Mathematical retroreflectors,, Discr. Contin. Dynam. Syst.-A, 30 (2011), 1211.
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), 16 (2010), 206.
|
[12] |
A. Plakhov and V. Roshchina, Invisibility in billiards,, Nonlinearity, 24 (2011), 847.
doi: 10.1088/0951-7715/24/3/007. |
[13] |
, "Invisibility,'', Wikipedia article. Available from: , (). Google Scholar |
[14] |
, "Unsichtbarkeit,'', Wikipedia article. Available from: , (). Google Scholar |
show all references
References:
[1] |
A. Aleksenko and A. Plakhov, Bodies of zero resistance and bodies invisible in one direction,, Nonlinearity, 22 (2009), 1247.
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.
|
[3] |
D. Bucur and G. Buttazzo, "Variational Methods in Shape Optimization Problems,", Birkhäuser (2005)., (2005).
|
[4] |
G. Buttazzo and B. Kawohl, On Newton's problem of minimal resistance,, Math. Intell., 15 (1993), 7.
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.
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.
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.
doi: 10.1002/1522-2616(200106)226:1<153::AID-MANA153>3.3.CO;2-U. |
[8] |
I. Newton, Philosophiae naturalis principia mathematica,, (1687)., (1687). Google Scholar |
[9] |
A. Plakhov, Scattering in billiards and problems of Newtonian aerodynamics,, Russ. Math. Surv., 64 (2009), 873.
doi: 10.1070/RM2009v064n05ABEH004642. |
[10] |
A. Plakhov, Mathematical retroreflectors,, Discr. Contin. Dynam. Syst.-A, 30 (2011), 1211.
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), 16 (2010), 206.
|
[12] |
A. Plakhov and V. Roshchina, Invisibility in billiards,, Nonlinearity, 24 (2011), 847.
doi: 10.1088/0951-7715/24/3/007. |
[13] |
, "Invisibility,'', Wikipedia article. Available from: , (). Google Scholar |
[14] |
, "Unsichtbarkeit,'', Wikipedia article. Available from: , (). Google Scholar |
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