Journal Menu
Volume 14, Issue 1 (2022) , Pages [1] - [119]
VISCOSITY SOLUTIONS FOR THE INHOMOGENEOUS RELATIVISTIC VLASOV EQUATION ON A SPHERICALLY SYMMETRIC GRAVITATIONAL FIELD SPACE-TIME
[1] R. D. Ayissi and R. M. Etoua, Optimal control problem and viscosity solutions for the Vlasov equation in Yang−Mills charged Bianchi models, Advances in Pure and Applied Mathematics 8(2) (2017), 129-140.
DOI: https://doi.org/10.1515/apam-2017-0001
[2] R. D. Ayissi, N. Noutchegueme, R. M. Etoua and H. P. M. Tchagna, Viscosity solutions for the one-body Liouville equation in Yang-Mills charged Bianchi models with non-zero mass, Letters in Mathematical Physics 105(9) (2015), 1289-1299.
DOI: https://doi.org/10.1007/s11005-015-0777-7
[3] G. Barles, Solutions de Viscosité des Équations de Hamilton-Jacobi,
[4] J. Binney and S. Tremaine, Galactic Dynamics,
[5] A. Bressan, Viscosity Solutions of Hamilton-Jacobi Equations and Optimal Control Problems, Advances in Pure and Applied Mathematics, 2001.
[6] C. Cercignani and G. M. Kremer, The Relativistic Boltzmann Equation: Theory and Applications,
DOI: https://doi.org/10.1007/978-3-0348-8165-4
[7] M. G. Crandall, L. C. Evans and P. L. Lions, Some properties of viscosity solutions of Hamilton-Jacobi equations, Transactions of the American Mathematical Society 282(2) (1984), 487-502.
DOI: https://doi.org/10.2307/1999247
[8] M. G. Crandall, H. Ishii and P. L. Lions, User’s guide to viscosity solutions of second order partial differential equation, Bulletin of the American Mathematical Society 27(1) (1992), 1-67.
DOI: https://doi.org/10.1090/S0273-0979-1992-00266-5
[9] M. G. Crandall and P. L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Transactions of the American Mathematical Society 277(1) (1983), 1-42.
DOI: https://doi.org/10.1090/S0002-9947-1983-0690039-8
[10] M. G. Crandall and P. L. Lions, Remarks on the existence and uniqueness of unbounded viscosity solutions of Hamilton-Jacobi equations, Technical Report, Wisconsin Univ-Madison Mathematics Research Center, 1985.
[11] D. David and F. K. Maturin, Viscosity solutions for the Vlasov equation in the presence of a Yang-Mills field in temporal gauge, African Diaspora Journal of Mathematics 23(1) (2020), 24-39.
[12] Y. C. Bruhat and N. Noutchegueme, Système de Yang-Mills-Vlasov en jauge temporelle, Annales de l’I.H.P. Physique Théorique 55(3) (1991), 759-787.
[13] L. C. Evans, Partial Differential Equations, A. M. S., 1997.
[14] G. Rein and A. D. Rendall, Global existence of solutions of the spherically symmetric Vlasov-Einstein system with small initial data, Communications in Mathematical Physics 150(3) (1992), 561-583.
DOI: https://doi.org/10.1007/BF02096962
[15] P. L. Lions, Generalized Solutions of Hamilton-Jacobi Equations, Research Notes in Mathematics 69 (1982).
[16] G. Rein, Static solutions of the spherically symmetric Vlasov-Einstein system, Mathematical Proceedings of the Cambridge Philosophical Society 115(3) (1994), 559-570.
DOI: https://doi.org/10.1017/S0305004100072303
[17] G. Rein, A. D. Rendall and J. Schaeffer, Critical collapse of collisionless matter: A numerical investigation, Physical Review D 58(4) (1998); Article 044007.
DOI: https://doi.org/10.1103/PhysRevD.58.044007
[18] A. D. Rendall, Cosmic censorship and the Vlasov equation, Classical and Quantum Gravity 9(8) (1992), 99-104.
DOI: https://doi.org/10.1088/0264-9381/9/8/005
[19] A. D. Rendall, Global properties of locally spatially homogeneous cosmological models with matter, Mathematical Proceedings of the Cambridge Philosophical Society 118(3) (1995), 511-526.
DOI: https://doi.org/10.1017/S0305004100073837
[20] A. D. Rendall, An introduction to the Einstein-Vlasov system, arXiv preprint grqc/9604001 (1996).
[21] A. D. Rendall and C. Uggla, Dynamics of spatially homogeneous locally rotationally symmetric solutions of the Einstein-Vlasov equations, Classical and Quantum Gravity 17(22) (2000), 4697-4714.
DOI: https://doi.org/10.1088/0264-9381/17/22/310
[22] E. Takou and F. L. C. Ciake, The relativistic Boltzmann equation on a spherically symmetric gravitational field, Classical and Quantum Gravity 34(19) (2017); Article 195006.
DOI: https://doi.org/10.1088/1361-6382/aa85d1
[23] G. Wolansky, Static solutions of the Vlasov-Einstein system, Archive for Rational Mechanics and Analysis 156(3) (2001), 205-230.