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Markus Kunze

Contact Research Teaching Publications


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

  • Papers:

  • IMPORTANT NOTES: The files to download are preprints but not the final versions that did appear or that are to appear. Some of the papers are best viewed at magnification 0.707, some do not contain the figures.
    1. M. Kunze: On the uniqueness and asymptotic behaviour
           of plasma corners,
           Z. Anal. Anwendungen 13, 629-644 (1994)

    2. M. Kunze: On a special class of nonlinear integral equations,
           J. Integral Equations Appl. 7, 329-350 (1995)

    3. M. Kunze: On zeros of semicondensing operators,
           Nonlinear Anal. 26, 313-321 (1996)

    4. 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)

    5. M. Kunze: A nonlinear characterization of Hilbert spaces,
           J. Math. Anal. Appl. 204, 627-630 (1996)

    6. M. Kunze & M.D.P. Monteiro Marques: Yosida-Moreau regularization
           of sweeping processes with unbounded variation,
           J. Differential Equations 130, 292-306 (1996)

    7. M. Kunze: A note on a paper of Cellina concerning
           differential equations in Banach spaces,
           Bull. London Math. Soc. 28, 613-616 (1996)

    8. M. Kunze & T. Küpper: Qualitative bifurcation analysis
           of a non-smooth friction-oscillator model,
           Z. Angew. Math. Phys. 48, 87-101 (1997)

    9. 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)

    10. M. Kunze & M.D.P. Monteiro Marques: Existence of solutions
            for degenerate sweeping processes,
            J. Convex Anal. 4, 165-176 (1997)

    11. M. Kunze & M.D.P. Monteiro Marques: BV solutions
            to evolution problems with time-dependent domains,
            Set-Valued Anal. 5, 57-72 (1997)

    12. 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)

    13. M. Kunze, T. Küpper & J. You: On the application of KAM theory
            to discontinuous dynamical systems,
            J. Differential Equations 139, 1-21 (1997)

    14. M. Kunze & G. Schlüchtermann: Strongly generated Banach spaces
            and measures of non-compactness,
            Math. Nachrichten 191, 197-214 (1998)

    15. M. Kunze & M.D.P. Monteiro Marques: Discretization methods
            for degenerate sweeping processes,
            Portugaliae Mathematica 55, 219-232 (1998)

    16. 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)

    17. M. Kunze: Instability of the periodic motion of a particle interacting
            with a scalar wave field,
            Comm. Math. Phys. 195, 509-523 (1998)

    18. M. Kunze: Unbounded solutions in non-smooth dynamical systems
            at resonance,
            Z. Ang. Math. Mech. 78, Supplement 3, S985-S986 (1998)

    19. 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)

    20. 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

    21. M. Kunze: Periodic solutions of nonlinear kinematic hardening models,
            Math. Meth. Appl. Sci. 22, 515-529 (1999)

    22. M. Kunze, T. Küpper, V.K. Mezentsev, E.G. Shapiro & S. Turitsyn:
            Nonlinear solitary waves with Gaussian tails,
            Physica D 128, 273-295 (1999)

    23. M. Kunze: Periodic solutions of conservative non-smooth
            dynamical systems,
            Z. Ang. Math. Mech. 79, Supplement 1, S97-S100 (1999)

    24. A. Komech, M. Kunze & H. Spohn: Effective dynamics
            for a mechanical particle coupled to a wave field,
            Comm. Math. Phys. 203, 1-19 (1999)

    25. 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

    26. M. Kunze, T. Küpper & Y. Li: On Conley index theory
            for non-smooth dynamical systems,
            Differential Integral Equations 13, 479-502 (2000)

    27. 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)

    28. 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

    29. 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)

    30. M. Kunze & H. Spohn: Radiation reaction and center manifolds,
            SIAM J. Math. Anal. 32, 30-53 (2000)

    31. M. Kunze & H. Spohn: Slow motion of charges interacting through
            the Maxwell field,
            Comm. Math. Phys. 212, 437-467 (2000)

    32. 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

    33. 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

    34. M. Kunze & H. Spohn: Adiabatic limit for the
            Abraham-Lorentz equations,
            Ann. H. Poincaré 1, 625-653 (2000)

    35. 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

    36. 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

    37. M. Kunze, T. Küpper & B. Liu: Boundedness and unboundedness
            of solutions for reversible oscillators at resonance,
            Nonlinearity 14, 1105-1122 (2001)

    38. M. Kunze: Bifurcation from the continuous spectrum
            without sign condition on the nonlinearity,
            Proc. Roy. Soc. Edinburgh, Ser. A 131, 927-943 (2001)

    39. 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)

    40. M. Kunze & A.D. Rendall: The Vlasov-Poisson system
            with radiation damping,
            Ann. H. Poincaré 2, 857-886 (2001)

    41. 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)

    42. M. Kunze & A.D. Rendall: Simplified models of electromagnetic
            and gravitational radiation damping,
            Classical Quantum Gravity 18, 3573-3587 (2001)

    43. M. Kunze & H. Spohn: Post-Coulombian dynamics at order c^{-3},
            J. Nonlinear Science 11, 321-396 (2001)

    44. 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


    45. 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

    46. M. Kunze: The singular perturbation limit of a variational problem
            from nonlinear fiber optics,
            Phys. D 180, 108-114 (2003)

    47. M. Kunze: On the existence of a maximizer for the Strichartz inequality,
            Comm. Math. Phys. 243, 137-162 (2003)

    48. M. Kunze: On a variational problem with lack of compactness related
            to the Strichartz inequality,
            Calc. Var. Partial Differential Equations 19, 307-336 (2004)

    49. 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)

    50. 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)

    51. M. Kunze & R. Ortega: On the number of solutions
            to semilinear boundary value problems,
            Adv. Nonlinear Stud. 4, 237-249 (2004)

    52. 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)

    53. S. Bauer & M. Kunze: The Darwin approximation
            of the relativistic Vlasov-Maxwell system,
            Ann. H. Poincaré 6, 283-308 (2005)

    54. M. Kunze & G. Schneider: Estimates for the KdV-limit
            of the Camassa-Holm equation,
            Lett. Math. Phys. 72, 17-26 (2005)

    55. A. Komech, E. Kopylova & M. Kunze: Dispersive estimates
            for 1D discrete Schrödinger and Klein-Gordon equations,
            Appl. Anal. 85, 1487-1508 (2006)

    56. 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)

    57. 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

    58. M. Kunze: Mathematical results related to dispersion management
            in nonlinear optical fibers,
            Oberwolfach Reports 4, 2628-2630 (2007)

    59. M. Kunze & R. Ortega: Complete orbits for twist maps on the plane,
            Ergodic Theory Dynam. Systems 28, 1197-1213 (2008)

    60. M. Kunze: Multipole radiation in classical particle systems,
            Oberwolfach Reports 5, 389-392 (2008)

    61. H. Andreasson, M. Kunze & G. Rein: Global existence
            for the spherically symmetric Einstein-Vlasov system
            with outgoing matter,
            Comm. Partial Differential Equations 33, 656-668 (2008)

    62. 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) [Strauss anniversary volume]

    63. M. Kunze & R. Ortega: Complete orbits for twist maps on the plane:
            extensions and applications,
            to appear in J. Dynamics Differential Equations [R. Johnson anniversary volume]

    64. M. Kunze: On the absence of radiationless motion for a rotating classical charge,
            Adv. Math. 223, 1632-1665 (2010)

    65. H. Andréasson, M. Kunze & G. Rein: The formation of black holes
            in spherically symmetric gravitational collapse,
            Math. Ann. 350, 683-705 (2011)

    66. M. Kunze & R. Ortega: Complete orbits for twist maps on the plane:
            the case of small twist,
            to appear in Ergodic Theory Dynam. Systems

    67. H. Andréasson, M. Kunze & G. Rein: Existence of axially symmetric static solutions
            of the Einstein-Vlasov system,
            to appear in Comm. Math. Phys.

    68. M. Kunze & D.M.A. Stuart: Nekhoroshev type stability results for Hamiltonian systems
            with an additional transversal component,
            submitted


      Theses:

      1. Das relativistische Vlasov-Maxwell-System partieller Differential-
             gleichungen zu Anfangsdaten mit nichtkompaktem Träger,
             Diploma thesis, Ludwig Maximilians-Universität München 1991 (238 pp.)

      2. 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.)

      3. 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.)

      4. Non-Smooth Dynamical Systems
             Habilitation thesis, Universität zu Köln 1998 (153 pp.)

      Last updated: 22 June 2011

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