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  • 1
    Electronic Resource
    Electronic Resource
    A stability result for the relativistic Vlasov-Maxwell system (1992)
    Springer
    Archive for rational mechanics and analysis 121 (1992), S. 187-203 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider a space-periodic version of the relativistic Vlasov-Maxwell system describing a collisionless plasma consisting of electrons and positively charged ions. As our main result, we prove that certain spacially homogeneous stationary solutions are nonlinearly stable. To this end we also establish global existence of weak solutions to the corresponding initial value problem. Our investigation is motivated by a corresponding result for the Vlasov-Poisson system, cf. [1, 14].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00375417
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  • 2
    Electronic Resource
    Electronic Resource
    Global existence of classical solutions to the vlasov-poisson system in a three-dimensional, cosmological setting (1994)
    Springer
    Archive for rational mechanics and analysis 126 (1994), S. 183-201 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The initial-value problem for the Vlasov-Poisson system is by now well understood in the case of an isolated system where, by definition, the distribution function of the particles as well as the gravitational potential vanish at spatial infinity. Here we start with homogeneous solutions, which have a spatially constant, non-zero mass density and which describe the mass distribution in a Newtonian model of the universe. These homogeneous states can be constructed explicitly, and we consider deviations from such homogeneous states, which then satisfy a modified version of the Vlasov-Poisson system. We prove global existence and uniqueness of classical solutions to the corresponding initial-value problem for initial data which represent spatially periodic deviations from homogeneous states.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00391558
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  • 3
    Electronic Resource
    Electronic Resource
    Linear stability of stationary solutions of the Vlasov-Poisson system in three dimensions (1995)
    Springer
    Archive for rational mechanics and analysis 130 (1995), S. 163-182 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Rigorous results on the stability of stationary solutions of the Vlasov-Poisson system are obtained in the contexts of both plasma physics and stellar dynamics. It is proved that stationary solutions in the plasma physics (stellar dynamics) case are linearly stable if they are decreasing (increasing) functions of the local, i.e., particle, energy. The main tool in the analysis is the free energy, a conserved quantity of the linearized system. In addition, an appropriate global existence result is proved for the linearized Vlasov-Poisson system and the existence of stationary solutions which satisfy the above stability condition is established.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00375154
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Stable Steady States in Stellar Dynamics (1999)
    Springer
    Archive for rational mechanics and analysis 147 (1999), S. 225-243 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract . We prove the existence and nonlinear stability of steady states of the Vlasov‐Poisson system in the stellar dynamics case. The steady states are obtained as minimizers of an energy‐Casimir functional from which fact their dynamical stability is deduced. The analysis applies to some of the well‐known polytropic steady states, but it also considerably extends the class of known steady states.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002050050150
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  • 5
    Electronic Resource
    Electronic Resource
    Generic global solutions of the relativistic Vlasov-Maxwell system of plasma physics (1990)
    Springer
    Communications in mathematical physics 135 (1990), S. 41-78 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The behaviour of classical solutions of the relativistic Vlasov-Maxwell system under small perturbations of the initial data is investigated. First it is shown that the solutions depend continuoussly on the initial data with respect to various norms. The main result is on global solutions: A global solution whose electromagnetic field decays in a certain way for large times is shown to remain global under small perturbations of the initial data and to retain the decay behaviour of the field. Therefore, such global solutions are generic. This result implies the existence of global solutions for nearly symmetric initial data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02097656
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  • 6
    Electronic Resource
    Electronic Resource
    A regularity theorem for solutions of the spherically symmetric Vlasov-Einstein system (1995)
    Springer
    Communications in mathematical physics 168 (1995), S. 467-478 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We show that if a solution of the spherically symmetric Vlasov-Einstein system develops a singularity at all then the first singularity has to appear at the center of symmetry. The main tool is an estimate which shows that a solution is global if all the matter remains away from the center of symmetry.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02101839
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  • 7
    Electronic Resource
    Electronic Resource
    Flat Steady States in Stellar Dynamics – Existence and Stability (1999)
    Springer
    Communications in mathematical physics 205 (1999), S. 229-247 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract: We consider a special case of the three dimensional Vlasov–Poisson system where the particles are restricted to a plane, a situation that is used in astrophysics to model extremely flattened galaxies. We prove the existence of steady states of this system. They are obtained as minimizers of an energy-Casimir functional from which fact a certain dynamical stability property is deduced. From a mathematics point of view these steady states provide examples of singular solutions of the three dimensional Vlasov–Poisson system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002200050674
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  • 8
    Electronic Resource
    Electronic Resource
    A rigorous stability result for the Vlasov-Poisson system in three dimensions (1993)
    Springer
    Annali di matematica pura ed applicata 164 (1993), S. 133-154 
    Details
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is proven that in a neutral two-component plasma with space homogeneous positively charged background, which is governed by the Vlasov-Poisson system and for which Poisson's equation is considered on a cube inR 3 with periodic boundary conditions, the space homogeneous stationary solutions g with energy gradient ∂g/∂ε ≤ 0 and compact support are (nonlinearly) stable in the L1-norm with respect to weak solutions of the initial value problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01759319
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  • 9
    Electronic Resource
    Electronic Resource
    Über Melanoblastome der Papille und Tumoren des retinalen Pigmentepithels (1960)
    Springer
    Graefe's archive for clinical and experimental ophthalmology 161 (1960), S. 519-531 
    Details
    ISSN: 1435-702X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Zusammenfassung Bei einem 55 Jahre alten Mann wird der linke Bulbus wegen eines pigmentierten Tumors der Papille enucleiert. Der histologische Befund ist in zweifacher Hinsicht bemerkenswert: 1. Es liegt eines der äußerst seltenen primären Melanoblastome der Papille vor. 2. Das histologische Bild der Geschwulst weist überraschend neurogene Züge auf. Melanoblastome von diesem Typus sind in dieser Lokalisation nie beobachtet worden. Es bestehen überzeugende Gründe für die Annahme eines vom retinalen P. E. ausgehenden Tumors. Dadurch erhält die vorliegende Beobachtung ihre besondere Bedeutung. Denn die Frage, ob das P. E. der Retina überhaupt Geschwülste zu produzieren vermag, gilt als bisher nicht endgültig geklärt.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00686428
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  • 10
    Electronic Resource
    Electronic Resource
    A two-species plasma in the limit of large ion mass (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 13 (1990), S. 159-167 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Classical solutions of the relativistic Vlasov-Maxwell system are considered, describing a collisionless plasma with two species of particles. ions and electrons. It is shown that as the ion mass m tends to infinity, the corresponding solution of the relativistic Vlasov-Maxwell system tends to the solution of a system, in which the ions are given by a fixed ion background and only the electrons move. The convergence is uniform on compact time intervals, with an asymptotic convergence rate of m-1.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670130206
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    Paper (German National Licenses)
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