On a relativistic Fokker-Planck equation in kinetic theory
Pages: 401 - 426,
Volume 4,
Issue 2,
June 2011
doi:10.3934/krm.2011.4.401 Abstract
References
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José Antonio Alcántara - Departamento de Matemática Aplicada, Facultad de ciencias, Universidad de Granada, 18071 Granada, Spain (email)
Simone Calogero - Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain (email)
| 1 |
F. Andreu, V. Caselles, J. M. Mazón and S. Moll, Finite propagation speed for limited flux diffusion equations, Arch. Ration. Mech. Anal., 182 (2006), 269-297. |
|
| 2 |
M. Bostan and T. Goudon, Low field regime for the relativistic Vlasov-Maxwell-Fokker-Planck system; the one and one half dimensional case, Kinet. Relat. Models, 1 (2008), 139-170. |
|
| 3 |
F. Bouchut and J. Dolbeault, On long time asymptotics of the Vlasov-Fokker-Planck equation and of the Vlasov-Poisson-Fokker-Planck system with coulombic and Newtonian potentials, Diff. Integ. Eqs., 8 (1995), 487-514. |
|
| 4 |
S. Calogero, Spherical symmetric steady states of galactic dynamics in scalar gravity, Class. Quant. Grav., 20 (2003), 1729-1741. |
|
| 5 |
S. Calogero, Global classical solutions to the 3D Nordström-Vlasov system, Comm. Math. Phys., 266 (2006), 343-353. |
|
| 6 |
S. Calogero, O. Sánchez and J. Soler, Asymptotic behavior and orbital stability of galactic dynamics in relativistic scalar gravity, Arch. Rat. Mech. Anal., 194 (2009), 743-773. |
|
| 7 |
S. Calogero, J. Calvo, O. Sánchez and J. Soler, Virial inequalities for steady states in relativistic galactic dynamics, Nonlinearity, 23 (2010), 1851-1871. |
|
| 8 |
S. Calogero, Exponential convergence to equilibrium for kinetic Fokker-Planck equations on Riemannian manifolds, preprint, arXiv:1009.5086. |
|
| 9 |
J. A. Carrillo, P. Laurençot and J. Rosado, Fermi-Dirac-Fokker-Planck equation: Well-posedness $&$ long-time asymptotics, J. Diff. Eqns., 247 (2009), 2209-2234. |
|
| 10 |
G. Chac\'on-Acosta and G. M. Kramer, Fokker-Planck-type equations for a simple gas and for a semirelativistic Brownian motion from a relativistic kinetic theory, Phys. Rev. E., 76 (2007), 021201. |
|
| 11 |
S. Chandrasekhar, Stochastic problems in physics and astronomy, Rev Mod. Phys., 15 (1943), 1-89. |
|
| 12 |
F. Debbasch and C. Chevalier, Relativistic stochastic processes: A review, AIP Conf. Proc., 913 (2007), 42-48. |
|
| 13 |
J. Dolbeault, Free energy and solutions of the Vlasov-Poisson-Fokker-Planck system: External potential and confinement (large time behavior and steady states), J. Math. Pures Appl., 78 (1999), 121-157. |
|
| 14 |
K. Dressler, Steady states in plasma physics-the Vlasov-Fokker-Planck equation, Math. Meth. Appl. Sci., 12 (1990), 471-487. |
|
| 15 |
K. Dressler, Stationary solutions of the Vlasov-Fokker-Planck equation, Math. Meth. Appl. Sci., 9 (1987), 169-176. |
|
| 16 |
J. Dunkel and P. Hänggi, Theory of the relativistic Brownian motion: The (1+3)-dimensional case, Phys. Rev. E, 72 (2005), 036106. |
|
| 17 |
J. Dunkel and P. Hänggi, Relativistic Brownian motion, Phys. Rep., 471 (2009), 1-73. |
|
| 18 |
D. T. Frank, "Nonlinear Fokker-Planck Equations: Fundamentals and Applications," Springer Series in Synergetics 25, Springer-Verlag, New York, 2005. |
|
| 19 |
R. T. Glassey, J. Schaeffer and Y. Zheng, Steady states of the Vlasov-Poisson-Fokker-Planck system, J. Math. An. Appl., 202 (1996), 1058-1075. |
|
| 20 |
Z. Haba, Relativistic diffusion, Phys. Rev. E, 79 (2009), 021128. |
|
| 21 |
Z. Haba, Relativistic diffusion of elementary particles with spin, Journ. Phys. A, 42 (2009), 445401. |
|
| 22 |
Z. Haba, Energy and entropy of relativistic diffusing particles, Mod. Phys. Lett. A, 25 (2010), 2683-2695. |
|
| 23 |
Z. Haba, Relativistic diffusive transport, preprint arXiv:0911.3126. |
|
| 24 |
B. Helffer and F. Nier, "Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators And Witten Laplacians," Lecture Notes in Mathematics 1862, Springer-Verlag, New York, 2000. |
|
| 25 |
L. Hörmander, Pseudodifferential operators and non-elliptic boundary problems, Ann. of Math., 83 (1966), 129-209. |
|
| 26 |
F. John, Blow-up for quasi linear wave equations in three space dimensions, Comm. Pure Appl. Math., 34 (1981), 29-51. |
|
| 27 |
I. Karatzas and S. E. Shreve, "Brownian Motion and Stochastic Calculus," Graduate Texts in Mathematics 113 2nd edition, Springer-Verlag, New York, 1991. |
|
| 28 |
C. R. Lai, On the one-and-one-half-dimensional relativistic Vlasov-Maxwell-Fokker-Planck system with non-vanishing viscosity, Math. Meth. Appl. Sci., 21 (1998), 1287-1296. |
|
| 29 |
E. H. Lieb and M. Loss, "Analysis," American Math. Soc. 14, Providence, 1997. |
|
| 30 |
C.-P. Ma and E. Bertschinger, A cosmological kinetic theory for the evolution of cold dark matter halos with substructure: Quasi-linear theory, The Astroph. J., 612 (2004), 28-49. |
|
| 31 |
M. Risken, "The Fokker-Planck Equation: Methods of Solutions and Applications," Springer Series in Synergetics 18, Springer-Verlag, Berlin, 1996. |
|
| 32 |
M. Schunck, M. Hegmann and E. Sedlmayr, The influence of stochastic density fluctuations on the infrared emissions of interstellar dark clouds, Mon. Noti. Royal Astron. Soc., 374 (2007), 949-959. |
|
| 33 |
S. L. Shapiro and S. A. Teukolsky, Scalar gravitation: A laboratory for numerical relativity, Phys. Rev. D, 47 (1993), 1529-1540. |
|
| 34 |
C. Sogge, "Lectures on Nonlinear Wave Equations," International Press, Cambridge, 1995. |
|
| 35 |
J. L. Vázquez, "The Porous Medium Equation: Mathematical Theory," Oxford Math. Monogr., Clarendon Press/Oxford Univ. Press, Oxford 2007. |
|
| 36 |
T. Yang and H. Yu, Global classical solutions for the Vlasov-Maxwell-Fokker-Planck system, SIAM J. Math. Anal., 42 (2010), 459-488. |
|
| 37 |
C. Villani Hypocoercivity, Memoirs of the AMS, 202 (2009), n. 950. |
|
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