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Existence of periodic solutions of a system of damped wave equations in thin domains
A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds
1. | SISSA, via Beirut 2-4, 34014 Trieste, Italy |
2. | SISSA, via Beirut 2-4 34014 Trieste |
3. | Institut de Mathématiques Élie Cartan de Nancy, UMR 7502 INRIA/Universités de Nancy/CNRS, POB 239, 54506 Vandoeuvre-lès-Nancy, France |
[1] |
Eric L. Grinberg, Haizhong Li. The Gauss-Bonnet-Grotemeyer Theorem in space forms. Inverse Problems and Imaging, 2010, 4 (4) : 655-664. doi: 10.3934/ipi.2010.4.655 |
[2] |
Daniel Genin, Serge Tabachnikov. On configuration spaces of plane polygons, sub-Riemannian geometry and periodic orbits of outer billiards. Journal of Modern Dynamics, 2007, 1 (2) : 155-173. doi: 10.3934/jmd.2007.1.155 |
[3] |
Mrinal Kanti Roychowdhury. Least upper bound of the exact formula for optimal quantization of some uniform Cantor distributions. Discrete and Continuous Dynamical Systems, 2018, 38 (9) : 4555-4570. doi: 10.3934/dcds.2018199 |
[4] |
M. Delgado-Téllez, Alberto Ibort. On the geometry and topology of singular optimal control problems and their solutions. Conference Publications, 2003, 2003 (Special) : 223-233. doi: 10.3934/proc.2003.2003.223 |
[5] |
Ellina Grigorieva, Evgenii Khailov, Andrei Korobeinikov. Optimal control for an epidemic in populations of varying size. Conference Publications, 2015, 2015 (special) : 549-561. doi: 10.3934/proc.2015.0549 |
[6] |
Changjun Yu, Lei Yuan, Shuxuan Su. A new gradient computational formula for optimal control problems with time-delay. Journal of Industrial and Management Optimization, 2022, 18 (4) : 2469-2482. doi: 10.3934/jimo.2021076 |
[7] |
Anthony M. Bloch, Rohit Gupta, Ilya V. Kolmanovsky. Neighboring extremal optimal control for mechanical systems on Riemannian manifolds. Journal of Geometric Mechanics, 2016, 8 (3) : 257-272. doi: 10.3934/jgm.2016007 |
[8] |
Miguel-C. Muñoz-Lecanda. On some aspects of the geometry of non integrable distributions and applications. Journal of Geometric Mechanics, 2018, 10 (4) : 445-465. doi: 10.3934/jgm.2018017 |
[9] |
Bing Sun. Optimal control of transverse vibration of a moving string with time-varying lengths. Mathematical Control and Related Fields, 2022, 12 (3) : 733-746. doi: 10.3934/mcrf.2021042 |
[10] |
Relinde Jurrius, Ruud Pellikaan. On defining generalized rank weights. Advances in Mathematics of Communications, 2017, 11 (1) : 225-235. doi: 10.3934/amc.2017014 |
[11] |
Minoru Murai, Waichiro Matsumoto, Shoji Yotsutani. Representation formula for the plane closed elastic curves. Conference Publications, 2013, 2013 (special) : 565-585. doi: 10.3934/proc.2013.2013.565 |
[12] |
Ke Wei, Jian-Feng Cai, Tony F. Chan, Shingyu Leung. Guarantees of riemannian optimization for low rank matrix completion. Inverse Problems and Imaging, 2020, 14 (2) : 233-265. doi: 10.3934/ipi.2020011 |
[13] |
Anulekha Dhara, Aparna Mehra. Conjugate duality for generalized convex optimization problems. Journal of Industrial and Management Optimization, 2007, 3 (3) : 415-427. doi: 10.3934/jimo.2007.3.415 |
[14] |
Mohammad Hadi Noori Skandari, Marzieh Habibli, Alireza Nazemi. A direct method based on the Clenshaw-Curtis formula for fractional optimal control problems. Mathematical Control and Related Fields, 2020, 10 (1) : 171-187. doi: 10.3934/mcrf.2019035 |
[15] |
Alexander Nabutovsky and Regina Rotman. Lengths of geodesics between two points on a Riemannian manifold. Electronic Research Announcements, 2007, 13: 13-20. |
[16] |
Isabeau Birindelli, Enrico Valdinoci. On the Allen-Cahn equation in the Grushin plane: A monotone entire solution that is not one-dimensional. Discrete and Continuous Dynamical Systems, 2011, 29 (3) : 823-838. doi: 10.3934/dcds.2011.29.823 |
[17] |
Juan Campos, Rafael Ortega. Location of fixed points and periodic solutions in the plane. Discrete and Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 517-523. doi: 10.3934/dcdsb.2008.9.517 |
[18] |
Dubi Kelmer. Approximation of points in the plane by generic lattice orbits. Journal of Modern Dynamics, 2017, 11: 143-153. doi: 10.3934/jmd.2017007 |
[19] |
Di Wu, Yanqin Bai, Fusheng Xie. Time-scaling transformation for optimal control problem with time-varying delay. Discrete and Continuous Dynamical Systems - S, 2020, 13 (6) : 1683-1695. doi: 10.3934/dcdss.2020098 |
[20] |
Rashad M. Asharabi, Jürgen Prestin. Computing eigenpairs of two-parameter Sturm-Liouville systems using the bivariate sinc-Gauss formula. Communications on Pure and Applied Analysis, 2020, 19 (8) : 4143-4158. doi: 10.3934/cpaa.2020185 |
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