-
Previous Article
Crack growth with non-interpenetration: A simplified proof for the pure Neumann problem
- DCDS Home
- This Issue
-
Next Article
An existence and uniqueness result for flux limited diffusion equations
On the regularization of the collision solutions of the one-center problem with weak forces
1. | BCAM - Basque Center for Applied Mathematics, Bizkaia Technology Park, 48160 Derio, Bizkaia,, Spain |
2. | Università di Milano Bicocca, Dipartimento di Matematica e Applicazioni, Via Cozzi 53, 20125 Milano |
References:
[1] |
S. J. Aarseth, Dynamical evolution of clusters of galaxies I, Monthly Notices of the Royal Astronomical Society, 126 (1963), 223-255. |
[2] |
V. Barutello, D. L. Ferrario and S. Terracini, On the singularities of generalized solutions to $n$-body-type problems, Int. Math. Res. Not. IMRN, (2008), Art. ID rnn 069, 78 pp. |
[3] |
G. Bellettini, G. Fusco and G. F. Gronchi, Regularization of the two-body problem via smoothing the potential, Commun. Pure Appl. Anal., 2 (2003), 323-353.
doi: 10.3934/cpaa.2003.2.323. |
[4] |
E. De Giorgi, Conjectures concerning some evolution problems, A celebration of John F. Nash, Jr., Duke Math. J., 81 (1996), 255-268.
doi: 10.1215/S0012-7094-96-08114-4. |
[5] |
C. C. Dyer and P. S. S. Ip, Softening in N-body simulations of collisionless systems, Astrophysical Journal, 409 (1993), 60-67.
doi: 10.1086/172641. |
[6] |
R. Easton, Regularization of vector fields by surgery, J. Differential Equations, 10 (1971), 92-99. |
[7] |
D. L. Ferrario and S. Terracini, On the existence of collisionless equivariant minimizers for the classical $n$-body problem, Invent. Math., 155 (2004), 305-362.
doi: 10.1007/s00222-003-0322-7. |
[8] |
W. B. Gordon, A minimizing property of Keplerian orbits, Amer. J. Math., 99 (1977), 961-971.
doi: 10.2307/2373993. |
[9] |
L. Hernquist and J. E. Barnes, Are some n-body algorithms intrinsically less collisional than others?, Astrophysical Journal, 349 (1990), 562-569.
doi: 10.1086/168343. |
[10] |
P. Kustaanheimo and E. Stiefel, Perturbation theory of Kepler motion based on spinor regularization, J. Reine Angew. Math., 218 (1965), 204-219.
doi: 10.1515/crll.1965.218.204. |
[11] |
T. Levi-Civita, Sur la régularisation du problème des trois corps, Acta Math., 42 (1920), 99-144.
doi: 10.1007/BF02404404. |
[12] |
R. McGehee, Double collisions for a classical particle system with nongravitational interactions, Comment. Math. Helv., 56 (1981), 524-557.
doi: 10.1007/BF02566226. |
[13] |
J. Moser, Regularization of Kepler's problem and the averaging method on a manifold, Comm. Pure Appl. Math., 23 (1970), 609-636.
doi: 10.1002/cpa.3160230406. |
[14] |
C. L. Siegel and J. K. Moser, "Lectures on Celestial Mechanics," Classics in Mathematics, Springer-Verlag, Berlin, 1995. |
[15] |
C. Stoica and A. Font, Global dynamics in the singular logarithmic potential, J. Phys. A, 36 (2003), 7693-7714.
doi: 10.1088/0305-4470/36/28/302. |
[16] |
V. G. Szebehely, "Theory of Orbits -- The Restricted Problem of Three Bodies," Academic Press, New York, 1967. |
[17] |
J. Touma and S. Tremaine, A map for eccentric orbits in non-axisymmetric potentials, MNRAS, 292 (1997), 905-932. |
[18] |
E. T. Whittaker, "A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: With an Introduction to the Problem of Three Bodies," 4th edition, Cambridge University Press, New York, 1959. |
show all references
References:
[1] |
S. J. Aarseth, Dynamical evolution of clusters of galaxies I, Monthly Notices of the Royal Astronomical Society, 126 (1963), 223-255. |
[2] |
V. Barutello, D. L. Ferrario and S. Terracini, On the singularities of generalized solutions to $n$-body-type problems, Int. Math. Res. Not. IMRN, (2008), Art. ID rnn 069, 78 pp. |
[3] |
G. Bellettini, G. Fusco and G. F. Gronchi, Regularization of the two-body problem via smoothing the potential, Commun. Pure Appl. Anal., 2 (2003), 323-353.
doi: 10.3934/cpaa.2003.2.323. |
[4] |
E. De Giorgi, Conjectures concerning some evolution problems, A celebration of John F. Nash, Jr., Duke Math. J., 81 (1996), 255-268.
doi: 10.1215/S0012-7094-96-08114-4. |
[5] |
C. C. Dyer and P. S. S. Ip, Softening in N-body simulations of collisionless systems, Astrophysical Journal, 409 (1993), 60-67.
doi: 10.1086/172641. |
[6] |
R. Easton, Regularization of vector fields by surgery, J. Differential Equations, 10 (1971), 92-99. |
[7] |
D. L. Ferrario and S. Terracini, On the existence of collisionless equivariant minimizers for the classical $n$-body problem, Invent. Math., 155 (2004), 305-362.
doi: 10.1007/s00222-003-0322-7. |
[8] |
W. B. Gordon, A minimizing property of Keplerian orbits, Amer. J. Math., 99 (1977), 961-971.
doi: 10.2307/2373993. |
[9] |
L. Hernquist and J. E. Barnes, Are some n-body algorithms intrinsically less collisional than others?, Astrophysical Journal, 349 (1990), 562-569.
doi: 10.1086/168343. |
[10] |
P. Kustaanheimo and E. Stiefel, Perturbation theory of Kepler motion based on spinor regularization, J. Reine Angew. Math., 218 (1965), 204-219.
doi: 10.1515/crll.1965.218.204. |
[11] |
T. Levi-Civita, Sur la régularisation du problème des trois corps, Acta Math., 42 (1920), 99-144.
doi: 10.1007/BF02404404. |
[12] |
R. McGehee, Double collisions for a classical particle system with nongravitational interactions, Comment. Math. Helv., 56 (1981), 524-557.
doi: 10.1007/BF02566226. |
[13] |
J. Moser, Regularization of Kepler's problem and the averaging method on a manifold, Comm. Pure Appl. Math., 23 (1970), 609-636.
doi: 10.1002/cpa.3160230406. |
[14] |
C. L. Siegel and J. K. Moser, "Lectures on Celestial Mechanics," Classics in Mathematics, Springer-Verlag, Berlin, 1995. |
[15] |
C. Stoica and A. Font, Global dynamics in the singular logarithmic potential, J. Phys. A, 36 (2003), 7693-7714.
doi: 10.1088/0305-4470/36/28/302. |
[16] |
V. G. Szebehely, "Theory of Orbits -- The Restricted Problem of Three Bodies," Academic Press, New York, 1967. |
[17] |
J. Touma and S. Tremaine, A map for eccentric orbits in non-axisymmetric potentials, MNRAS, 292 (1997), 905-932. |
[18] |
E. T. Whittaker, "A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: With an Introduction to the Problem of Three Bodies," 4th edition, Cambridge University Press, New York, 1959. |
[1] |
G. Bellettini, G. Fusco, G. F. Gronchi. Regularization of the two-body problem via smoothing the potential. Communications on Pure and Applied Analysis, 2003, 2 (3) : 323-353. doi: 10.3934/cpaa.2003.2.323 |
[2] |
Boumediene Abdellaoui, Ahmed Attar. Quasilinear elliptic problem with Hardy potential and singular term. Communications on Pure and Applied Analysis, 2013, 12 (3) : 1363-1380. doi: 10.3934/cpaa.2013.12.1363 |
[3] |
Vasile Mioc, Ernesto Pérez-Chavela. The 2-body problem under Fock's potential. Discrete and Continuous Dynamical Systems - S, 2008, 1 (4) : 611-629. doi: 10.3934/dcdss.2008.1.611 |
[4] |
Nicolas Forcadel, Cyril Imbert, Régis Monneau. Homogenization of some particle systems with two-body interactions and of the dislocation dynamics. Discrete and Continuous Dynamical Systems, 2009, 23 (3) : 785-826. doi: 10.3934/dcds.2009.23.785 |
[5] |
Xiumei Deng, Jun Zhou. Global existence and blow-up of solutions to a semilinear heat equation with singular potential and logarithmic nonlinearity. Communications on Pure and Applied Analysis, 2020, 19 (2) : 923-939. doi: 10.3934/cpaa.2020042 |
[6] |
Vladimir Georgiev, Sandra Lucente. Focusing nlkg equation with singular potential. Communications on Pure and Applied Analysis, 2018, 17 (4) : 1387-1406. doi: 10.3934/cpaa.2018068 |
[7] |
Scipio Cuccagna, Masaya Maeda. On weak interaction between a ground state and a trapping potential. Discrete and Continuous Dynamical Systems, 2015, 35 (8) : 3343-3376. doi: 10.3934/dcds.2015.35.3343 |
[8] |
Laurence Cherfils, Stefania Gatti, Alain Miranville. A doubly nonlinear parabolic equation with a singular potential. Discrete and Continuous Dynamical Systems - S, 2011, 4 (1) : 51-66. doi: 10.3934/dcdss.2011.4.51 |
[9] |
Younghun Hong. Strichartz estimates for $N$-body Schrödinger operators with small potential interactions. Discrete and Continuous Dynamical Systems, 2017, 37 (10) : 5355-5365. doi: 10.3934/dcds.2017233 |
[10] |
Shitao Liu, Roberto Triggiani. Determining damping and potential coefficients of an inverse problem for a system of two coupled hyperbolic equations. Part I: Global uniqueness. Conference Publications, 2011, 2011 (Special) : 1001-1014. doi: 10.3934/proc.2011.2011.1001 |
[11] |
David Gómez-Castro, Juan Luis Vázquez. The fractional Schrödinger equation with singular potential and measure data. Discrete and Continuous Dynamical Systems, 2019, 39 (12) : 7113-7139. doi: 10.3934/dcds.2019298 |
[12] |
Mouhamed Moustapha Fall, Veronica Felli. Unique continuation properties for relativistic Schrödinger operators with a singular potential. Discrete and Continuous Dynamical Systems, 2015, 35 (12) : 5827-5867. doi: 10.3934/dcds.2015.35.5827 |
[13] |
Pierluigi Colli, Gianni Gilardi, Gabriela Marinoschi, Elisabetta Rocca. Optimal control for a phase field system with a possibly singular potential. Mathematical Control and Related Fields, 2016, 6 (1) : 95-112. doi: 10.3934/mcrf.2016.6.95 |
[14] |
Pierluigi Colli, Gianni Gilardi, Gabriela Marinoschi, Elisabetta Rocca. Optimal control for a conserved phase field system with a possibly singular potential. Evolution Equations and Control Theory, 2018, 7 (1) : 95-116. doi: 10.3934/eect.2018006 |
[15] |
Yu Su. Ground state solution of critical Schrödinger equation with singular potential. Communications on Pure and Applied Analysis, 2021, 20 (10) : 3347-3371. doi: 10.3934/cpaa.2021108 |
[16] |
Kazuhiro Ishige, Y. Kabeya. Hot spots for the two dimensional heat equation with a rapidly decaying negative potential. Discrete and Continuous Dynamical Systems - S, 2011, 4 (4) : 833-849. doi: 10.3934/dcdss.2011.4.833 |
[17] |
Yulia Karpeshina and Young-Ran Lee. On polyharmonic operators with limit-periodic potential in dimension two. Electronic Research Announcements, 2006, 12: 113-120. |
[18] |
Chjan C. Lim, Joseph Nebus, Syed M. Assad. Monte-Carlo and polyhedron-based simulations I: extremal states of the logarithmic N-body problem on a sphere. Discrete and Continuous Dynamical Systems - B, 2003, 3 (3) : 313-342. doi: 10.3934/dcdsb.2003.3.313 |
[19] |
Fengming Ma, Yiju Wang, Hongge Zhao. A potential reduction method for the generalized linear complementarity problem over a polyhedral cone. Journal of Industrial and Management Optimization, 2010, 6 (1) : 259-267. doi: 10.3934/jimo.2010.6.259 |
[20] |
Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš. Positive solutions for perturbations of the Robin eigenvalue problem plus an indefinite potential. Discrete and Continuous Dynamical Systems, 2017, 37 (5) : 2589-2618. doi: 10.3934/dcds.2017111 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]