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Prof. Dr. Gerhard Rein Prof. Dr. Gerhard Rein
Prof. Dr. Gerhard Rein

Fakultät für Mathematik, Physik und Informatik
Mathematisches Institut


Arbeitsgebiete

Nichtlineare partielle Differentialgleichungen zur Beschreibung von großen Ensembles von Teilchen, die über selbstkonsistente Kräfte wechselwirken, z.B.

  • Vlasov-Poisson-System,
  • Vlasov-Maxwell-System,
  • Einstein-Vlasov-System,

motiviert durch Probleme aus der Astrophysik (Dynamik von Galaxien, Entstehung schwarzer Löcher) und der Plasmaphysik. Typische Fragestellungen:

  • Anfangswertproblem, lokale/globale Existenz,
  • stationäre Lösungen und ihre Stabilität bzw. Instabilität,
  • zeitlich periodische, pulsierende Lösungen,
  • Gravitationskollaps.

Profile


Prof. Dr. Gerhard Rein

Fakultät für Mathematik, Physik und Informatik
Mathematisches Institut


Publikationen

2021

Hadžić, Mahir; Lin, Zhiwu; Rein, Gerhard
Stability and instability of self-gravitating relativistic matter distributions
In: Archive for Rational Mechanics and Analysis Bd. 241 (2021) . - S. 1-89
doi:10.1007/s00205-021-01647-2 ...

Günther, Sebastian; Straub, Christopher; Rein, Gerhard
Collisionless Equilibria in General Relativity : Stable Configurations beyond the First Binding ...
In: The Astrophysical Journal Bd. 918 (2021) Heft 2. - S. 48
doi:10.3847/1538-4357/ac0eef ...

Günther, Sebastian; Körner, Jacob; Lebeda, Timo; Pötzl, Bastian; Rein, Gerhard; Straub, Christopher; Weber, Jörg
A numerical stability analysis for the Einstein–Vlasov system
In: Classical and Quantum Gravity Bd. 38 (2021) Heft 3. - S. No. 035003
doi:10.1088/1361-6382/abcbdf ...

2020

Rein, Gerhard; Straub, Christopher
On the transport operators arising from linearizing the Vlasov-Poisson or Einstein-Vlasov syste ...
In: Kinetic and Related Models Bd. 13 (2020) Heft 5. - S. 933-949
doi:10.3934/krm.2020032 ...

2018

Ramming, Tobias; Rein, Gerhard
Oscillating solutions of the Vlasov–Poisson system : A numerical investigation
In: Physica D: Nonlinear Phenomena Bd. 365 (2018) . - S. 72-79
doi:10.1016/j.physd.2017.10.013 ...

Rein, Gerhard
The asymptotic behavior of solutions to the repulsive n-body problem
In: SIAM Journal on Mathematical Analysis Bd. 50 (2018) Heft 1. - S. 1-4
doi:10.1137/17M1116271 ...

2017

Ramming, Tobias; Rein, Gerhard
Mass-radius spirals for steady state families of the Vlasov-Poisson system
In: Archive for Rational Mechanics and Analysis Bd. 224 (2017) Heft 3. - S. 1127-1159
doi:10.1007/s00205-017-1098-z ...

2016

Rein, Gerhard; Taegert, Lukas
Gravitational collapse and the Vlasov-Poisson system
In: Annales Henri Poincaré Bd. 17 (2016) Heft 6. - S. 1415-1427
doi:10.1007/s00023-015-0424-y ...

2015

Rein, Gerhard
Galactic dynamics in MOND : Existence of equilibria with finite mass and compact support
In: Kinetic and Related Models Bd. 8 (2015) Heft 2. - S. 381-394
doi:10.3934/krm.2015.8.381 ...

Andréasson, Håkan; Rein, Gerhard
On the rotation curves for axially symmetric disk solutions of the Vlasov-Poisson system
In: Monthly Notices of the Royal Astronomical Society Bd. 446 (2015) Heft 4. - S. 3932-3942
doi:10.1093/mnras/stu2346 ...

Hadžić, Mahir; Rein, Gerhard
On the small redshift limit of steady states of the spherically symmetric Einstein-Vlasov syste ...
In: Mathematical Proceedings of the Cambridge Philosophical Society Bd. 159 (2015) Heft 3. - S. 529-546
doi:10.1017/S0305004115000511 ...

2014

Andréasson, Håkan; Kunze, Markus; Rein, Gerhard
Rotating, stationary, axially symmetric spacetimes with collisionless matter
In: Communications in Mathematical Physics Bd. 329 (2014) Heft 2. - S. 787-808
doi:10.1007/s00220-014-1904-5 ...

2013

Korch, Matthias; Ramming, Tobias; Rein, Gerhard
Parallelization of particle-in-cell codes for nonlinear kinetic models from mathematical physic ...
International Conference on Parallel Processing, The 42nd Annual Conference ICPP 2013 : Proceedings ; 1 - 4 October 2013 Lyon, France
Los Alamitos, CA : IEEE, 2013. - S. 523-529
doi:10.1109/ICPP.2013.65 ...

Ramming, Tobias; Rein, Gerhard
Spherically symmetric equilibria for self-gravitating kinetic or fluid models in the non-relati ...
In: SIAM Journal on Mathematical Analysis Bd. 45 (2013) Heft 2. - S. 900-914
doi:10.1137/120896712 ...

Hadžić, Mahir; Rein, Gerhard
Stability for the spherically symmetric Einstein-Vlasov system : a coercivity estimate
In: Mathematical Proceedings of the Cambridge Philosophical Society Bd. 155 (2013) Heft 3. - S. 529-556
doi:10.1017/S030500411300056X ...

2011

Andréasson, Håkan; Kunze, Markus; Rein, Gerhard
Existence of axially symmetric static solutions of the Einstein-Vlasov system
In: Communications in Mathematical Physics Bd. 308 (2011) . - S. 23-47
doi:10.1007/s00220-011-1324-8 ...

Andréasson, Håkan; Kunze, Markus; Rein, Gerhard
The formation of black holes in spherically symmetric gravitational collapse
In: Mathematische Annalen Bd. 350 (2011) Heft 3. - S. 683-705
doi:10.1007/s00208-010-0578-3 ...

2010

Andréasson, Håkan; Rein, Gerhard
The asymptotic behaviour in Schwarzschild time of Vlasov matter in spherically symmetric gravit ...
In: Mathematical Proceedings of the Cambridge Philosophical Society Bd. 149 (2010) Heft 1. - S. 173-188
doi:10.1017/S0305004109990454 ...

Andréasson, Håkan; Rein, Gerhard
Formation of trapped surfaces for the spherically symmetric Einstein-Vlasov system
In: Journal of Hyperbolic Differential Equations Bd. 7 (2010) Heft 4. - S. 707-731
doi:10.1142/S0219891610002268 ...

Andréasson, Håkan; Kunze, Markus; Rein, Gerhard
Gravitational collapse and the formation of black holes for the spherically symmetric Einstein- ...
In: Quarterly of Applied Mathematics Bd. 68 (2010) Heft 1. - S. 17-42
http://www.ams.org/journals/qam/2010-68-01/S0033-5 ...

2009

Firt, Roman; Rein, Gerhard; Seehafer, Martin
Flat galaxies with dark matter halos : existence and stability
In: Communications in Mathematical Physics Bd. 291 (2009) Heft 1. - S. 225-255
doi:10.1007/s00220-009-0872-7 ...

Andréasson, Håkan; Rein, Gerhard; Eklund, Mikael
A numerical investigation of the steady states of the spherically symmetric Einstein-Vlasov-Max ...
In: Classical and Quantum Gravity Bd. 26 (2009) Heft 14
doi:10.1088/0264-9381/26/14/145003 ...

2008

Andréasson, Håkan; Kunze, Markus; Rein, Gerhard
Global existence for the spherically symmetric Einstein-Vlasov system with outgoing matter
In: Communications in Partial Differential Equations Bd. 33 (2008) Heft 4. - S. 656-668
doi:10.1080/03605300701454883 ...

2007

Rein, Gerhard
Collisionless Kinetic Equations from Astrophysics : The Vlasov-Poisson System
Dafermos,Constantine M.; Feireisl, E. (Hrsg.): Handbook of Differential Equations : Evolutionary Equations. Vol. 3
Amsterdam : Elsevier, 2007. - S. 383-476
doi:10.1016/S1874-5717(07)80008-9 ...

Hadžić, Mahir; Rein, Gerhard
Global existence and nonlinear stability for the relativistic Vlasov-Poisson system in the grav ...
In: Indiana University Mathematics Journal Bd. 56 (2007) Heft 5. - S. 2453-2488
doi:10.1512/iumj.2007.56.3064 ...

Guo, Yan; Rein, Gerhard
A non-variational approach to nonlinear stability in stellar dynamics applied to the King model
In: Communications in Mathematical Physics Bd. 271 (2007) Heft 2. - S. 489-509
doi:10.1007/s00220-007-0212-8 ...

Andréasson, Håkan; Rein, Gerhard
On the steady states of the spherically symmetric Einstein-Vlasov system
In: Classical and Quantum Gravity Bd. 24 (2007) Heft 7. - S. 1809-1832
doi:10.1088/0264-9381/24/7/008 ...

Firt, Roman; Rein, Gerhard
Stability of disk-like galaxies : Part I: Stability via reduction
In: Analysis Bd. 26 (2007) Heft 4. - S. 507-525
doi:10.1524/anly.2006.26.4.507 ...

2006

Bauer, Sebastian; Kunze, Markus; Rein, Gerhard; Rendall, Alan D.
Multipole radiation in a collisionless gas coupled to electromagnetism or scalar gravitation
In: Communications in Mathematical Physics Bd. 266 (2006) Heft 1. - S. 267-288
doi:10.1007/s00220-006-0015-3 ...

Andréasson, Håkan; Rein, Gerhard
A numerical investigation of the stability of steady states and critical phenomena for the sphe ...
In: Classical and Quantum Gravity Bd. 23 (2006) Heft 11. - S. 3659-3677
doi:10.1088/0264-9381/23/11/001 ...

2005

Andréasson, Håkan; Calogero, Simone; Rein, Gerhard
Global classical solutions to the spherically symmetric Nordström-Vlasov system
In: Mathematical Proceedings of the Cambridge Philosophical Society Bd. 138 (2005) Heft 3. - S. 533-539
doi:10.1017/S0305004105008467 ...

Rein, Gerhard
Nonlinear Stability of Newtonian Galaxies and Stars from a Mathematical Perspective
In: Annals of the New York Academy of Sciences Bd. 1045 (2005) . - S. 103-119
doi:10.1196/annals.1350.010 ...

Kunzinger, Michael; Rein, Gerhard; Steinbauer, Roland; Teschl, Gerald
On classical solutions of the relativistic Vlasov-Klein-Gordon system
In: Electronic Journal of Differential Equations Bd. 2005 (2005) Heft 1. - S. 1-17
http://www.emis.de/journals/EJDE/Volumes/2005/01/k ...

2004

Calogero, Simone; Rein, Gerhard
Global weak solutions to the Nordström-Vlasov system
In: Journal of Differential Equations Bd. 204 (2004) Heft 2. - S. 323-338
doi:10.1016/j.jde.2004.02.011 ...

Rein, Gerhard
Global weak solutions to the relativistic Vlasov-Maxwell system revisited
In: Communications in Mathematical Sciences Bd. 2 (2004) Heft 2. - S. 145-158
doi:10.4310/CMS.2004.v2.n2.a1 ...

Rein, Gerhard
On future geodesic completeness for the Einstein-Vlasov system with hyperbolic symmetry
In: Mathematical Proceedings of the Cambridge Philosophical Society Bd. 137 (2004) Heft 1. - S. 237-244
doi:10.1017/S0305004103007485 ...

2003

Rein, Gerhard; Rodewis, Thomas
Convergence of a particle-in-cell scheme for the spherically symmetric Vlasov-Einstein system
In: Indiana University Mathematics Journal Bd. 52 (2003) Heft 4. - S. 821-862
doi:10.1512/iumj.2003.52.2363 ...

Kunzinger, Michael; Rein, Gerhard; Steinbauer, Roland; Teschl, Gerald
Global weak solutions of the relativistic Vlasov-Klein-Gordon system
In: Communications in Mathematical Physics Bd. 238 (2003) Heft 1-2. - S. 367-378
doi:10.1007/s00220-003-0861-1 ...

Rein, Gerhard
Non-linear stability of gaseous stars
In: Archive for Rational Mechanics and Analysis Bd. 168 (2003) Heft 2. - S. 115-130
doi:10.1007/s00205-003-0260-y ...

Calogero, Simone; Rein, Gerhard
On classical solutions of the Nordström-Vlasov system
In: Communications in Partial Differential Equations Bd. 28 (2003) Heft 11-12. - S. 1863-1885
doi:10.1081/PDE-120025488 ...

Andréasson, Håkan; Rein, Gerhard; Rendall, Alan D.
On the Einstein-Vlasov system with hyperbolic symmetry
In: Mathematical Proceedings of the Cambridge Philosophical Society Bd. 134 (2003) Heft 3. - S. 529-549
doi:10.1017/S0305004102006606 ...

Guo, Yan; Rein, Gerhard
Stable models of elliptical galaxies
In: Monthly Notices of the Royal Astronomical Society Bd. 344 (2003) Heft 4. - S. 1296-1306
doi:10.1046/j.1365-8711.2003.06920.x ...

2002

Markowich, Peter A.; Rein, Gerhard; Wolansky, Gershon
Existence and nonlinear stability of steady states of the Schrödinger-Poisson system
In: Journal of Statistical Physics Bd. 106 (2002) Heft 5-6. - S. 1221-1239
doi:10.1023/A:1014050206769 ...

Rein, Gerhard
Reduction and a concentration-compactness principle for energy-Casimir functionals
In: SIAM Journal on Mathematical Analysis Bd. 33 (2002) Heft 4. - S. 896-912
doi:10.1137/P0036141001389275 ...

Rein, Gerhard
Stability of spherically symmetric steady states in galactic dynamics against general perturbat ...
In: Archive for Rational Mechanics and Analysis Bd. 161 (2002) Heft 1. - S. 27-42
doi:10.1007/s002050100167 ...

2001

Guo, Yan; Rein, Gerhard
Isotropic steady states in galactic dynamics
In: Communications in Mathematical Physics Bd. 219 (2001) . - S. 607-629
doi:10.1007/s002200100434 ...

Dolbeault, Jean; Rein, Gerhard
Time-dependent rescalings and Lyapunov functionals for the Vlasov-Poisson and Euler-Poisson sys ...
In: Mathematical Models and Methods in Applied Sciences Bd. 11 (2001) Heft 3. - S. 407-432
doi:10.1142/S021820250100091X ...

2000

Rein, Gerhard; Rendall, Alan D.
Compact support of spherically symmetric equilibria in non-relativistic and relativistic galac ...
In: Mathematical Proceedings of the Cambridge Philosophical Society Bd. 128 (2000) Heft 2. - S. 363-380

Rein, Gerhard
Stationary and static stellar dynamic models with axial symmetry
In: Nonlinear Analysis : Theory, Methods & Applications Bd. 41 (2000) Heft 3-4. - S. 313-344
doi:10.1016/S0362-546X(98)00280-6 ...

1999

Guo, Yan; Rein, Gerhard
Existence and stability of Camm type steady states in galactic dynamics
In: Indiana University Mathematics Journal Bd. 48 (1999) Heft 4. - S. 1237-1255
doi:10.1512/iumj.1999.48.1819 ...

Rein, Gerhard
Flat steady states in stellar dynamics : existence and stability
In: Communications in Mathematical Physics Bd. 205 (1999) Heft 1. - S. 229-247
doi:10.1007/s002200050674 ...

Braasch, Peter; Rein, Gerhard; Vukadinovic, Jesenko
Nonlinear stability of stationary plasmas : an extension of the energy-Casimir method
In: SIAM Journal on Applied Mathematics Bd. 59 (1999) Heft 3. - S. 831-844
doi:10.1137/S0036139997329069 ...

Guo, Yan; Rein, Gerhard
Stable steady states in stellar dynamics
In: Archive for Rational Mechanics and Analysis Bd. 147 (1999) Heft 3. - S. 225-243
doi:10.1007/s002050050150 ...

Rein, Gerhard
Static shells for the Vlasov-Poisson and Vlasov-Einstein systems
In: Indiana University Mathematics Journal Bd. 48 (1999) Heft 1. - S. 335-346
doi:10.1512/iumj.1999.48.1636 ...

1998

Rein, Gerhard; Rendall, Alan D.; Schaeffer, Jack
Critical collapse of collisionless matter : A numerical investigation
In: Physical Review D Bd. 58 (1998) . - S. 044007
doi:10.1103/PhysRevD.58.044007 ...

Rein, Gerhard
Growth estimates for the solutions of the Vlasov-Poisson system in the plasma physics case
In: Mathematische Nachrichten Bd. 191 (1998) Heft 1. - S. 269-278
doi:10.1002/mana.19981910114 ...

Batt, Jürgen; Kunze, Markus; Rein, Gerhard
On the asymptotic behaviour of a one-dimensional monocharged plasma and a rescaling method
In: Advances in Differential Equations Bd. 3 (1998) Heft 2. - S. 271-292

1997

Rein, Gerhard
Nonlinear stability of homogeneous models in Newtonian cosmology
In: Archive for Rational Mechanics and Analysis Bd. 140 (1997) Heft 4. - S. 335-351
doi:10.1007/s002050050070 ...

Rein, Gerhard
Selfgravitating systems in Newtonian theory : the Vlasov-Poisson system
In: Banach Center Publications Bd. 41 (1997) Heft 1. - S. 179-194
http://matwbn.icm.edu.pl/ksiazki/bcp/bcp41/bcp4111 ...

1996

Rein, Gerhard
Cosmological solutions of the Vlasov-Einstein system with spherical, plane, and hyperbolic symm ...
In: Mathematical Proceedings of the Cambridge Philosophical Society Bd. 119 (1996) Heft 4. - S. 739-762
doi:10.1017/S0305004100074569 ...

Rein, Gerhard; Rendall, Alan D.
Erratum: Global existence of solutions of the spherically symmetric Vlasov-Einstein system with ...
In: Communications in Mathematical Physics Bd. 176 (1996) Heft 2. - S. 475-478
doi:10.1007/BF02099559 ...

Illner, Reinhard; Rein, Gerhard
Time decay of the solutions of the Vlasov-Poisson system in the plasma physical case
In: Mathematical Methods in the Applied Sciences Bd. 19 (1996) Heft 17. - S. 1409-1413
doi:10.1002/(SICI)1099-1476(19961125)19:17<1409::A ...

1995

Batt, Jürgen; Morrison, Philip J.; Rein, Gerhard
Linear stability of stationary solutions of the Vlasov-Poisson system in three dimensions
In: Archive for Rational Mechanics and Analysis Bd. 130 (1995) Heft 2. - S. 163-182
doi:10.1007/BF00375154 ...

Rein, Gerhard; Rendall, Alan D.; Schaeffer, Jack
A regularity theorem for solutions of the spherically symmetric Vlasov-Einstein system
In: Communications in Mathematical Physics Bd. 168 (1995) Heft 3. - S. 467-478
doi:10.1007/BF02101839 ...

1994

Rein, Gerhard; Rendall, Alan D.
Global existence of classical solutions to the Vlasov-Poisson system in a three-dimensional, co ...
In: Archive for Rational Mechanics and Analysis Bd. 126 (1994) Heft 2. - S. 183-201
doi:10.1007/BF00391558 ...

Rein, Gerhard
Non-linear stability for the Vlasov-Poisson system : the energy-Casimir method
In: Mathematical Methods in the Applied Sciences Bd. 17 (1994) Heft 14. - S. 1129-1140
doi:10.1002/mma.1670171404 ...

Rein, Gerhard
Static solutions of the spherically symmetric Vlasov-Einstein system
In: Mathematical Proceedings of the Cambridge Philosophical Society Bd. 115 (1994) Heft 3. - S. 559-570
doi:10.1017/S0305004100072303 ...

1993

Batt, Jürgen; Rein, Gerhard
A rigorous stability result for the Vlasov-Poisson system in three dimensions
In: Anali di Matematica Pura ed Applicata Bd. 164 (1993) Heft 1. - S. 133-154
doi:10.1007/BF01759319 ...

Rein, Gerhard; Rendall, Alan D.
Smooth static solutions of the spherically symmetric Vlasov-Einstein system
In: Annales de l'Institut Henri Poincaré A Bd. 59 (1993) Heft 4. - S. 383-397
http://archive.numdam.org/ARCHIVE/AIHPA/AIHPA_1993 ...

1992

Rein, Gerhard
Existence of stationary, collisionless plasmas in bounded domains
In: Mathematical Methods in the Applied Sciences Bd. 15 (1992) Heft 5. - S. 365-374
doi:10.1002/mma.1670150507 ...

Rein, Gerhard; Weckler, Jürgen
Generic global classical solutions of the Vlasov-Fokker-Planck-Poisson system in three dimensio ...
In: Journal of Differential Equations Bd. 99 (1992) Heft 1. - S. 59-77
doi:10.1016/0022-0396(92)90135-A ...

Rein, Gerhard; Rendall, Alan D.
Global existence of solutions of the spherically symmetric Vlasov-Einstein system with small in ...
In: Communications in Mathematical Physics Bd. 150 (1992) Heft 3. - S. 561-583
doi:10.1007/BF02096962 ...

Rein, Gerhard; Rendall, Alan D.
The Newtonian limit of the spherically symmetric Vlasov-Einstein system
In: Communications in Mathematical Physics Bd. 150 (1992) Heft 3. - S. 585-591
doi:10.1007/BF02096963 ...

Kruse, Kai-Olaf; Rein, Gerhard
A stability result for the relativistic Vlasov-Maxwell system
In: Archive for Rational Mechanics and Analysis Bd. 121 (1992) Heft 2. - S. 187-203
doi:10.1007/BF00375417 ...

1991

Batt, Jürgen; Rein, Gerhard
Global classical solutions of the periodic Vlasov-Poisson system
In: Comptes Rendus de l'Académie des Sciences. Série I Bd. 313 (1991) . - S. 411-416

1990

Rein, Gerhard
Generic global solutions of the relativistic Vlasov-Maxwell system of plasma physics
In: Communications in Mathematical Physics Bd. 135 (1990) Heft 1. - S. 41-78
doi:10.1007/BF02097656 ...

Rein, Gerhard
A two-species plasma in the limit of large ion mass
In: Mathematical Methods in the Applied Sciences Bd. 13 (1990) Heft 2. - S. 159-167
doi:10.1002/mma.1670130206 ...

1987

Farin, Gerald; Rein, Gerhard; Sapidis, Nikolas; Worsey, Andrew
Fairing cubic b-spline curves
In: Computer Aided Geometric Design Bd. 4 (1987) Heft 1-2. - S. 91-103
doi:10.1016/0167-8396(87)90027-6 ...

Prof. Dr. Gerhard Rein

Fakultät für Mathematik, Physik und Informatik
Mathematisches Institut


Prof. Dr. Gerhard Rein
Professor

Lehrstuhl Mathematik VI
Gebäude NW II
Raum 3.2.01.539
Universität Bayreuth    
95440 Bayreuth   

Telefon: 0921/55-3287
E-Mail: Gerhard.Rein@uni-bayreuth.de

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Verantwortlich für die Redaktion: Univ.Prof.Dr. Gerhard Rein

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