Applied Mathematics

Books:

M. Kunze: Non-Smooth Dynamical Systems,
Lecture Notes in Mathematics Vol. 1744, Springer
Berlin-New York 2000

M. Kunze: A Birman-Schwinger Principle in Galactic Dynamics,
Birkhäuser/Springer, Cham 2021

Papers:

IMPORTANT NOTE: The files to download are preprints but not the final versions that did appear or that are to appear.

M. Kunze: On the uniqueness and asymptotic behaviour
of plasma corners,
Z. Anal. Anwendungen 13, 629-644 (1994)
M. Kunze: On a special class of nonlinear integral equations,
J. Integral Equations Appl. 7, 329-350 (1995)
M. Kunze: On zeros of semicondensing operators,
Nonlinear Anal. 26, 313-321 (1996)
M. Kunze & M.D.P. Monteiro Marques: B.V. solutions
to evolution problems with time-dependent domains,
C. R. Acad. Sci. Paris Sér. I Math. 323, 993-998 (1996)
M. Kunze: A nonlinear characterization of Hilbert spaces,
J. Math. Anal. Appl. 204, 627-630 (1996)
M. Kunze & M.D.P. Monteiro Marques: Yosida-Moreau regularization
of sweeping processes with unbounded variation,
J. Differential Equations 130, 292-306 (1996)
M. Kunze: A note on a paper of Cellina concerning
differential equations in Banach spaces,
Bull. London Math. Soc. 28, 613-616 (1996)
M. Kunze & T. Küpper: Qualitative bifurcation analysis
of a non-smooth friction-oscillator model,
Z. Angew. Math. Phys. 48, 87-101 (1997)
A. Komech, H. Spohn & M. Kunze: Long-time asymptotics for
a classical particle interacting with a scalar wave field,
Comm. Partial Differential Equations 22, 307-335 (1997)
M. Kunze & M.D.P. Monteiro Marques: Existence of solutions
for degenerate sweeping processes,
J. Convex Anal. 4, 165-176 (1997)
M. Kunze & M.D.P. Monteiro Marques: BV solutions
to evolution problems with time-dependent domains,
Set-Valued Anal. 5, 57-72 (1997)
M. Kunze & J. Neumann: Linear complementary problems
and the simulation of the motion of rigid body systems,
Z. Ang. Math. Mech. 77, 833-838 (1997)
M. Kunze, T. Küpper & J. You: On the application of KAM theory
to discontinuous dynamical systems,
J. Differential Equations 139, 1-21 (1997)
M. Kunze & G. Schlüchtermann: Strongly generated Banach spaces
and measures of non-compactness,
Math. Nachrichten 191, 197-214 (1998)
M. Kunze & M.D.P. Monteiro Marques: Discretization methods
for degenerate sweeping processes,
Portugaliae Mathematica 55, 219-232 (1998)
J. Batt, M. Kunze & G. Rein: On the asymptotic behaviour
of a one-dimensional, monocharged plasma and a rescaling method,
Advances in Differential Equations 3, 271-292 (1998)
M. Kunze: Instability of the periodic motion of a particle interacting
with a scalar wave field,
Comm. Math. Phys. 195, 509-523 (1998)
M. Kunze: Unbounded solutions in non-smooth dynamical systems
at resonance,
Z. Ang. Math. Mech. 78, Supplement 3, S985-S986 (1998)
M. Kunze & M.D.P. Monteiro Marques: On parabolic quasi-variational
inequalities and state-dependent sweeping processes,
Topological Methods in Nonlinear Analysis 12, 179-191 (1998)
M. Kunze & M.D.P. Monteiro Marques: Degenerate sweeping processes,
      in: Proc. IUTAM Symposium on Variations of Domains
      and Free-Boundary Problems in Solid Mechanics, Paris 1997,
      Eds. P. Argoul, M. Frémond & Q.S. Nguyen, Kluwer Acad. Press,
      Dordrecht 1999, pp. 301-307
M. Kunze: Periodic solutions of nonlinear kinematic hardening models,
Math. Meth. Appl. Sci. 22, 515-529 (1999)
M. Kunze, T. Küpper, V.K. Mezentsev, E.G. Shapiro & S. Turitsyn:
Nonlinear solitary waves with Gaussian tails,
Physica D 128, 273-295 (1999)
M. Kunze: Periodic solutions of conservative non-smooth
dynamical systems,
Z. Ang. Math. Mech. 79, Supplement 1, S97-S100 (1999)
A. Komech, M. Kunze & H. Spohn: Effective dynamics
for a mechanical particle coupled to a wave field,
Comm. Math. Phys. 203, 1-19 (1999)
M. Kunze & M.D.P. Monteiro Marques: A note on Lipschitz continuous
      solutions of a parabolic quasi-variational inequality,
      in: Luso-Chinese Symposium on Nonlinear Evolution Equations,
      Macau 1998, Eds. Ta-tsien Li, Long-wei Lin & J.F. Rodrigues
      World Scientific, Singapore-New Jersey-London 1999, pp. 109-115
M. Kunze, T. Küpper & Y. Li: On Conley index theory
for non-smooth dynamical systems,
Differential Integral Equations 13, 479-502 (2000)
M. Kunze: On Lyapunov exponents for non-smooth dynamical systems
with an application to a pendulum with dry friction,
J. Dynamics Differential Equations 12, 31-116 (2000)
M. Kunze: Rigorous methods and numerical results
      for dry friction problems,
      Chapter 9 of the book: M. Wiercigroch & B. de Kraker:
      Applied Nonlinear Dynamics and Chaos of Mechanical Systems with
      Discontinuities, World Scientific, Singapore-New Jersey-London 2000
M. Kunze & J.F. Rodrigues: An elliptic quasi-variational inequality
with gradient constraint and some of its applications,
Math. Meth. Appl. Sci. 23, 897-908 (2000)
M. Kunze & H. Spohn: Radiation reaction and center manifolds,
SIAM J. Math. Anal. 32, 30-53 (2000)
M. Kunze & H. Spohn: Slow motion of charges interacting through
the Maxwell field,
Comm. Math. Phys. 212, 437-467 (2000)
M. Kunze & M.D.P. Monteiro Marques: An introduction
      to Moreau's sweeping process,
      in: Impacts in Mechanical Systems - Analysis and Modelling,
      Ed. B. Brogliato, Lecture Notes in Physics Vol. 551, Springer,
      Berlin-New York 2000, pp. 1-60
M. Kunze: Effective dynamics for the Maxwell-Lorentz system,
      in: International Conference on Differential Equations (Equadiff 99),
      Berlin 1999, Eds. B. Fiedler, K. Gröger & J. Sprekels, Vol. 1,
      World Scientific, Singapore-New Jersey-London 1999, pp. 109-111
M. Kunze & H. Spohn: Adiabatic limit for the
Abraham-Lorentz equations,
Ann. H. Poincaré 1, 625-653 (2000)
M. Kunze: Remarks on boundedness of semilinear oscillators,
      in: Nonlinear Analysis and its Applications to Differential Equations,
      Lisbon 1998, Eds. M.R. Grossinho, M. Ramos, C. Rebelo & L. Sanchez,
      Progress in Nonlinear Differential Equations and Their Applications
      Vol. 43, Birkhäuser, Basel-Boston 2001, pp. 311-320
M. Kunze & T. Küpper: Nonsmooth dynamical systems: An overview,
      in: Ergodic Theory, Analysis, and Efficient Simulation
      of Dynamical Systems, Ed. B. Fiedler, Springer, Berlin-New York 2001,
      pp. 431-452
M. Kunze, T. Küpper & B. Liu: Boundedness and unboundedness
of solutions for reversible oscillators at resonance,
Nonlinearity 14, 1105-1122 (2001)
M. Kunze: Bifurcation from the continuous spectrum
without sign condition on the nonlinearity,
Proc. Roy. Soc. Edinburgh, Ser. A 131, 927-943 (2001)
M. Kunze: Periodic solutions of a singular Lagrangian system
related to dispersion-managed fiber communication devices,
Nonlinear Dynamics and Systems Theory 1, 159-167 (2001)
M. Kunze & A.D. Rendall: The Vlasov-Poisson system
with radiation damping,
Ann. H. Poincaré 2, 857-886 (2001)
M. Kunze: On the period of periodic motions of a particle
in a scalar wave field,
Z. Ang. Math. Mech. 81, Supplement 3, S603-S606 (2001)
M. Kunze & A.D. Rendall: Simplified models of electromagnetic
and gravitational radiation damping,
Classical Quantum Gravity 18, 3573-3587 (2001)
M. Kunze & H. Spohn: Post-Coulombian dynamics at order c^{-3},
J. Nonlinear Science 11, 321-396 (2001)
M. Kunze & H. Spohn: Slow motion of charges interacting
      through the Maxwell field,
      in: XIIIth International Congress on Mathematical Physics,
      London 2000, Eds. A. Grigoryan, A. Fokas, T. Kibble & B. Zegarlinski,
      International Press, Boston 2001, pp. 219-224
M. Kunze: Infinitely many radial solutions of a variational problem
related to dispersion-managed optical fibers,
Proc. AMS 131, 2181-2188 (2003)
M. Kunze & B. Michaeli: On the rigorous applicability
      of Oseledets' theorem to obtain Lyapunov exponents
      for non-smooth dynamical systems,
      to appear (!?) in Proc. 2. Int. Conf. Diff. Equ., Marrakesh 1995,
      Ed. O. Arino
M. Kunze: The singular perturbation limit of a variational problem
from nonlinear fiber optics,
Phys. D 180, 108-114 (2003)
M. Kunze: On the existence of a maximizer for the Strichartz inequality,
Comm. Math. Phys. 243, 137-162 (2003)
M. Kunze: On a variational problem with lack of compactness related
to the Strichartz inequality,
Calc. Var. Partial Differential Equations 19, 307-336 (2004)
Th. Brand, M. Kunze, G. Schneider & Th. Seelbach: Hopf bifurcation
and exchange of stability in diffusive media,
Arch. Rat. Mech. Anal. 171, 263-296 (2004)
M. Kunze & G. Schneider: Exchange of stability
      and finite-dimensional dynamics in a bifurcation problem
      with marginally stable continuous spectrum,
      Z. Angew. Math. Phys. 55, 383-399 (2004)
M. Kunze & R. Ortega: On the number of solutions
to semilinear boundary value problems,
Adv. Nonlinear Stud. 4, 237-249 (2004)
M. Kunze, J. Moeser & V. Zharnitsky: Ground states
      for the higher order dispersion managed NLS equation
      in the absence of average dispersion,
      J. Differential Equations 209, 77-100 (2005)
S. Bauer & M. Kunze: The Darwin approximation
of the relativistic Vlasov-Maxwell system,
Ann. H. Poincaré 6, 283-308 (2005)
M. Kunze & G. Schneider: Estimates for the KdV-limit
of the Camassa-Holm equation,
Lett. Math. Phys. 72, 17-26 (2005)
A. Komech, E. Kopylova & M. Kunze: Dispersive estimates
for 1D discrete Schrödinger and Klein-Gordon equations,
Appl. Anal. 85, 1487-1508 (2006)
S. Bauer, M. Kunze, G. Rein & A.D. Rendall: Multipole radiation
in a collisionless gas coupled to electromagnetism or scalar gravitation,
Comm. Math. Phys. 266, 267-288 (2006)
S. Bauer & M. Kunze: Radiative friction for charges interacting with the
      Maxwell field: Classical many-particle systems,
      in: Analysis, Modeling and Simulation of Multiscale Problems,
      Ed. A. Mielke, Springer, Berlin-New York 2006, pp. 531-551
M. Kunze: Mathematical results related to dispersion management
in nonlinear optical fibers,
Oberwolfach Reports 4, 2628-2630 (2007)
M. Kunze & R. Ortega: Complete orbits for twist maps on the plane,
Ergodic Theory Dynam. Systems 28, 1197-1213 (2008)
M. Kunze: Multipole radiation in classical particle systems,
Oberwolfach Reports 5, 389-392 (2008)
H. Andréasson, M. Kunze & G. Rein: Global existence
      for the spherically symmetric Einstein-Vlasov system
      with outgoing matter,
      Comm. Partial Differential Equations 33, 656-668 (2008)
H. Andréasson, M. Kunze & G. Rein: Gravitational collapse
      and the formation of black holes for the spherically symmetric
      Einstein-Vlasov system,
      Quarterly Applied. Math. 68, 17-42 (2010) [W. Strauss anniversary volume]
M. Kunze: On the absence of radiationless motion for a rotating classical charge,
Adv. Math. 223, 1632-1665 (2010)
H. Andréasson, M. Kunze & G. Rein: The formation of black holes
in spherically symmetric gravitational collapse,
Math. Ann. 350, 683-705 (2011)
M. Kunze & R. Ortega: Complete orbits for twist maps on the plane:
extensions and applications,
J. Dynamics Differential Equations 23, 405-423 (2011) [R. Johnson anniversary volume]
M. Kunze & R. Ortega: Complete orbits for twist maps on the plane:
the case of small twist,
Ergodic Theory Dynam. Systems 31, 1471-1498 (2011)
H. Andréasson, M. Kunze & G. Rein: Existence of axially symmetric static solutions
of the Einstein-Vlasov system,
Comm. Math. Phys. 308, 23-47 (2011)
M. Kunze & R. Ortega: Twist mappings with non-periodic angles,
      in: Stability and Bifurcation Theory for Non-Autonomous Differential Equations,
      Lecture Notes in Mathematics Vol. 2065,
      Eds. R. Johnson & M.P. Pera, Springer, Berlin-New York 2013, pp. 265-300
M. Kunze & R. Ortega: Long-time stability estimates
for the non-periodic Littlewood boundedness problem,
Proc. London Math. Soc. 107, 39-75 (2013)
H. Andréasson, M. Kunze & G. Rein: Rotating, stationary, axially symmetric
spacetimes with collisionless matter,
Comm. Math. Phys. 329, 787-808 (2014)
M. Kunze & D.M.A. Stuart: Nekhoroshev type stability results for Hamiltonian systems
with an additional transversal component,
J. Math. Anal. Appl. 419, 1351-1386 (2014)
H.M. Huynh & M. Kunze: Partner orbits and action differences on compact factors
of the hyperbolic plane. Part I: Sieber-Richter pairs,
Nonlinearity 28, 593-623 (2015)
M. Kunze: Yet another criterion for global existence
in the 3D relativistic Vlasov-Maxwell system,
J. Differential Equations 259, 4413-4442 (2015)
M. Kunze & R. Ortega: Almost surely recurrent motions in the Euclidean space,
Proc. Amer. Math. Soc. 145, 4345-4351 (2017)
M. Kunze: Higher regularity of the 'tangential' fields
in the relativistic Vlasov-Maxwell system,
J. Differential Equations 265, 2778-2792 (2018)
H. Andréasson & M. Kunze: Comments on the paper 'Static solutions
of the Vlasov-Einstein system' by G. Wolansky,
Arch. Rat. Mech. Anal. 235, 783-791 (2019)
M. Kunze & R. Ortega: Escaping orbits are rare
in the quasi-periodic Fermi-Ulam ping-pong,
Ergodic Theory Dynam. Systems 40, 975-991 (2020)
M. Kunze & R. Ortega: Growth rates of orbits in non-periodic twist maps
and a theorem by Neishtadt,
Nonlinearity 34, 3732-3761 (2021)
M. Kunze & R. Ortega: Hamiltonian normal forms and applications to maps,
also available from http://www.ugr.es/~ecuadif/fuentenueva.htm
M. Kunze: A second look at the Kurth solution
in galactic dynamics, R. Glassey memorial issue,
Kinet. Relat. Models 15, 651-662 (2022)
M. Kunze: A Birman-Schwinger principle in galactic dynamics:
ESI, Vienna, 07-11 February 2022,
Classical Quantum Gravity 39, 244001 (2022)
H. Andréasson & M. Kunze: Static solutions to the spherically symmetric Einstein-Vlasov system:
a particle-number-Casimir approach,
to appear in SIAM J. Math. Anal.
É. Amorim, H. Andréasson & M. Kunze: Proof of the Einstein quadrupole formula for solutions of the
Einstein-Vlasov system close to Minkowski spacetime,
also available from https://arxiv.org/abs/2309.00431

Theses:

Das relativistische Vlasov-Maxwell-System partieller Differential-
gleichungen zu Anfangsdaten mit nichtkompaktem Träger,
Diploma thesis, Ludwig Maximilians-Universität München 1991 (238 pp.)
Beiträge zur Theorie halbverdichtender Operatoren in Banachräumen
     mit einer Anwendung auf ein freies Randwertproblem aus der
     Plasmaphysik,
     Ph.D. thesis, Ludwig Maximilians-Universität München 1994 (133 pp.)
Contributions to the Theory of Semicondensing Vectorfields
     in Banach spaces with an Application to a Free Boundary Problem
     Arising in Plasma Physics
     (english translation of 2.)
Non-Smooth Dynamical Systems
Habilitation thesis, Universität zu Köln 1998 (153 pp.)

Last updated: September 04, 2023