Publications of Roland Schnaubelt

Here you find the list of my publications including links to the PDFs of the preprints. (Back to my home page.) 

  1. C. Bresch, R. Schnaubelt: Local wellposedness of Maxwell systems with scalar-type retarded material laws.  NoDEA Nonlinear Differential Equations Appl. 33  (2026), paper no. 13, 33 pp. PDF for download.
  2. S. Nicaise, R. Schnaubelt: Maxwell equations with localized internal damping: strong and polynomial stability. Commun. Anal. Mech. 17 (2025), 849-877. PDF for download.
  3. M. Ruff, R. Schnaubelt: Error analysis of the Lie splitting for semilinear wave equations with finite-energy solutions. Discrete Contin. Dyn. Syst. 45 (2025), 2969-3008. PDF for download.
  4. V. Müller, R. Schnaubelt, Y. Tomilov: On growth and instability for semilinear evolution equations: an abstract approach. Math. Ann. 389 (2024), 3885-3933. PDF for download.
  5. R. Nutt, R. Schnaubelt: Normal trace inequalities and decay of solutions to the nonlinear Maxwell system with absorbing boundary. J. Math. Anal. Appl. 532 (2024), paper no. 127915, 35 pp. PDF for download.
  6. R. Schippa, R. Schnaubelt: Strichartz estimates for Maxwell equations in media: the fully anisotropic case. J. Hyperbolic Differ. Equ. 20 (2023), 917-966.  PDF for download.
  7. R. Schippa, R. Schnaubelt: Strichartz estimates for Maxwell equations in media: the structured case in two dimensions. Archiv Math. 121 (2023), 425-436. PDF for download.
  8. S. Ohrem, W. Reichel, R. Schnaubelt: Well-posedness for a (1+1)-dimensional wave equation with quasilinear boundary condition. Nonlinearity 36 (2023), 6712-6746. PDF for download.
  9. T. Dohnal, R. Schnaubelt, D. Tietz: Rigorous envelope approximation for interface wave-packets in Maxwell's equations with 2D localization. SIAM J. Math. Anal. 55 (2023), 6898-6939. PDF for download.
  10. R. Schippa, R. Schnaubelt: On quasilinear Maxwell equations in two dimensions. Pure Appl. Anal. 4 (2022), 313-365. PDF for download.
  11. S. Fornaro, G. Metafune, D. Pallara, R. Schnaubelt: Multi-dimensional degenerate operators in L^p-spaces. Commun. Pure Appl. Anal. 21 (2022), 2115-2145. PDF for download.
  12. P. D'Ancona, R. Schnaubelt: Global Strichartz estimates for an inhomogeneous Maxwell system. Comm. Partial Differential Equations 47 (2022), 630-675. PDF for download.
  13. R. Schnaubelt, M. Spitz: Local wellposedness of quasilinear Maxwell equations with conservative interface conditions. Commun. Math. Sci. 20 (2022), 2115-2145. PDF for download.
  14. S. Fornaro, G. Metafune, D. Pallara, R. Schnaubelt: L^p-spectrum of degenerate hypoelliptic Ornstein-Uhlenbeck operators. J. Funct. Anal. 280 (2021), paper no. 108807, 22 pp. PDF for download.
  15. R. Schnaubelt, M. Spitz: Local wellposedness of quasilinear Maxwell equations with absorbing boundary conditions. Evol. Equ. Control Theory 10 (2021), 155-198. PDF for download. 
  16. S. Herr, T. Lamm, T. Schmid, R. Schnaubelt: Biharmonic wave maps: Local wellposedness in high regularity. Nonlinearity 33 (2020), 2270-2305. PDF for download.
  17. M. Pokojovy, R. Schnaubelt: Boundary stabilization of quasilinear Maxwell equations. J. Differential Equations 268 (2020), 784-812. PDF for download.
  18. S. Herr, T. Lamm, R. Schnaubelt: Biharmonic wave maps into spheres. Proc. Amer. Math. Soc. 148 (2020), 787-796. PDF for download.
  19. I. Lasiecka, M. Pokojovy, R. Schnaubelt: Exponential decay of quasilinear Maxwell equations with interior conductivity. NoDEA Nonlinear Differential Equations Appl. 26 (2019), Paper No. 51, 34 pp. PDF for download.
  20. J. Eilinghoff, T. Jahnke, R. Schnaubelt: Error analysis of an energy preserving ADI splitting scheme for the Maxwell equations. SIAM J. Numer. Anal. 57 (2019), 1036-1057. PDF for download.
  21. L. Rzepnicki, R. Schnaubelt: Polynomial stability for a system of coupled strings. Bull. London Math. Soc. 50 (2018), 1117-1136. PDF for download.
  22. J. Eilinghoff, R. Schnaubelt: Error analysis  of an ADI splitting scheme for the inhomogeneous Maxwell equations. Discrete Contin. Dyn. Syst. Ser. A.  38 (2018), 5685-5709. PDF for download.
  23. P. D'Ancona, S. Nicaise, R. Schnaubelt: Blow-up for nonlinear Maxwell equations. Electron. J. Differential Equations 2018, paper no. 73, 9 pp. PDF for download.
  24. M. Hochbruck, T. Pazur, R. Schnaubelt: Error analysis of implicit Runge-Kutta methods for quasilinear hyperbolic evolution equations. Numer. Math. 138 (2018), 557–579. PDF for download.
  25. T. Jahnke, M. Mikl, R. Schnaubelt: Strang splitting for a semilinear Schrödinger equation with damping and forcing. J. Math. Anal. Appl. 455 (2017), 1051-1071. PDF for download.
  26. Y. Latushkin, R. Schnaubelt, Xinyao Yang: Stable foliations near a traveling front for reaction diffusion systems. Discrete Contin. Dyn. Syst. Ser. B. 22 (2017), 3145-3165. PDF for download.
  27. R. Schnaubelt, M. Veraar: Regularity of stochastic Volterra equations by functional calculus methods. J. Evol. Equ. 17 (2017), 523-536. PDF for download.
  28. L. Maniar, M. Meyries, R. Schnaubelt: Null controllability for parabolic problems with dynamic boundary conditions of reactive-diffusive type. Evol. Equ. Control Theory 6 (2017), 381–407. PDF for download.
  29. R. Schnaubelt: Stable and unstable manifolds for quasilinear parabolic problems with fully nonlinear dynamical boundary conditions. Adv. Differential Equations 22 (2017), 541-592. PDF for download.
  30. J. Eilinghoff, R. Schnaubelt, K. Schratz: Fractional error estimates of splitting schemes for the nonlinear Schrödinger equation. J. Math. Anal. Appl. 442 (2016), 740-760. PDF for download.
  31. L. Lorenzi, A. Lunardi, R. Schnaubelt: Strong convergence of solutions to nonautonomous Kolmogorov equations. Proc. Amer. Math. Soc. 144 (2016), 3903-3917. PDF for download.
  32. W. Dörfler, H. Gerner,  R. Schnaubelt: Local wellposedness of a quasilinear wave equation. Appl. Anal. 95 (2016), 2110-2123. PDF for download.
  33. E.M. Ait Benhassi, S. Boulite, L. Maniar, R. Schnaubelt: Polynomial internal and external stability of well-posed linear systems. In: W. Arendt, R. Chill and Y. Tomilov (Eds.), "Operator Semigroups meet Complex Analysis, Harmonic Analysis and Mathematical Physics (Proceedings Herrnhut 2013)," Birkhäuser, 2015, pp. 1-15. PDF for download.
  34. R. Denk, R. Schnaubelt: A structurally damped plate equation with Dirichlet-Neumann boundary conditions. J. Differential Equations 259 (2015), 1323-1353. PDF for download.
  35. D. Hundertmark, P. Kunstmann, R. Schnaubelt: Stability of dispersion managed solitons for vanishing average dispersion. Archiv Math. 104 (2015), 283-288. PDF for download.
  36. M. Hochbruck, T. Jahnke, R. Schnaubelt: Convergence of an ADI splitting for Maxwells equations. Numer. Math. 129 (2015), 535-561. PDF for download.
  37. S. Fornaro, G. Metafune, D. Pallara, R. Schnaubelt: Second order elliptic operators in L_2 with first order degeneration at the boundary and outward pointing drift. Commun. Pure Appl. Anal. 14 (2015), 407-419. PDF for download.
  38. R. Schnaubelt: Center manifolds and attractivity for quasilinear parabolic problems with fully nonlinear dynamical boundary conditions. Discrete  Contin. Dyn. Syst. Ser. A 35 (2015), 1193-1230. PDF for download.
  39. R. Johnson, Y. Latushkin, R. Schnaubelt: Reduction principle and asymptotic phase for center manifolds  of parabolic systems with nonlinear boundary conditions. J. Dynam. Differential Equations 26 (2014), 243-266. PDF for download.
  40. M. Baroun, B. Jacob, L. Maniar, R. Schnaubelt: Semilinear observation systems. Systems Control Lett. 62 (2013), 924-929. PDF for download.
  41. S. Fornaro, G. Metafune, D. Pallara, R. Schnaubelt: One-dimensional degenerate operators in L^p-spaces. J. Math. Anal. Appl. 402 (2013), 308-318. PDF for download.
  42. M. Meyries, R. Schnaubelt: Maximal regularity with temporal weights for parabolic problems with inhomogeneous boundary conditions. Math. Nachr. 285 (2012), 1032-1051. PDF for download.
  43. M. Meyries, R. Schnaubelt: Interpolation, embeddings and traces of anisotropic fractional Sobolev spaces with temporal weights. J. Funct. Anal. 262 (2012), 1200-1229. PDF for download.
  44. S. Fornaro, G. Metafune, D. Pallara, R. Schnaubelt: Degenerate operators of Tricomi type in L^p-spaces and in spaces of continuous functions. J. Differential Equations 252 (2012), 1182-1212. PDF for download.
  45. L. Maniar, R. Schnaubelt: Stability of periodic solutions to  parabolic problems with nonlinear boundary conditions. Adv. Differential Equations 17 (2012), 557-604. PDF for download.
  46. R. Schnaubelt, M. Veraar: Stochastic equations with boundary noise.  J. Escher et.al. (Eds.), "Parabolic Problems:  Herbert Amann Festschrift," Birkhäuser, 2011, pp. 609-629. PDF for download.
  47. R. Schnaubelt, G. Weiss: Two classes of passive time-varying well-posed  linear systems. Math. Control Signals Systems 21 (2010), 265-301. PDF for download.
  48. M. Geissert, L. Lorenzi, R. Schnaubelt: L^p-regularity for parabolic operators with unbounded time-dependent coefficients. Ann. Mat. Pura Appl. (4) 189 (2010), 303-333. PDF for download.
  49. R. Schnaubelt, M. Veraar: Structurally damped plate and wave equations with random point force in arbitrary space dimensions. Differential Integral Equations 23 (2010), 957-988. PDF for download.
  50. G. Metafune, D. Pallara, P.J. Rabier, R. Schnaubelt: Uniqueness for elliptic operators on L^p(R^N) with unbounded coefficients. Forum Math. 22 (2010), 583-601. PDF for download.
  51. M. Baroun, L. Maniar, R. Schnaubelt: Almost periodicity and Fredholmity of parabolic evolution equations  with inhomogeneous boundary values. Integral Equations Operator Theory 65 (2009), 169-193. PDF for download.
  52. M. Hieber, L. Lorenzi, J. Prüss, A. Rhandi, R. Schnaubelt: Global properties of generalized Ornstein-Uhlenbeck operators on L^p(R^N,R^N) with more than linearly growing coefficients. J. Math. Anal. Appl. 350 (2009), 100-121. PDF for download.
  53. J. Prüss, R. Schnaubelt, Rico Zacher: Global asymptotic stability of equilibria in models for virus dynamics. Math. Model. Nat. Phenom. 3 (2008), 126-142. PDF for download. 
  54. L. Maniar, R. Schnaubelt: Robustness of  Fredholm  properties of parabolic evolution equations under boundary perturbations. J. Lond. Math. Soc. (2) 77 (2008), 558-580. PDF for download.
  55. Y. Latushkin, J. Prüss, R. Schnaubelt: Center manifolds and dynamics near equilibria of quasilinear parabolic systems with fully nonlinear boundary conditions. Discrete  Contin. Dyn. Syst. Ser. B 9 (2008), 595-633. PDF for download. 
  56. S. Hadd, A. Rhandi, R. Schnaubelt: Feedbacks for time varying regular linear systems with input and state delays. IMA J. Math. Control Inform. 25 (2008), 85-110. PDF for download.
  57. L. Maniar, R. Schnaubelt: The Fredholm alternative for parabolic evolution equations with inhomogeneous boundary conditions. J. Differential Equations 235 (2007), 308-339. PDF for download.
  58. B. Jacob, R. Schnaubelt: Observability of polynomially stable systems. Systems Control Lett. 56 (2007), 277-284. PDF for download.
  59. Y. Latushkin, A. Pogan, R. Schnaubelt: Dichotomy and Fredholm properties of evolution equations. J. Operator Theory 58 (2007), 387-414. PDF for download. 
  60. Y. Latushkin, J. Prüss, R. Schnaubelt: Stable and unstable manifolds for quasilinear parabolic systems  with fully nonlinear boundary conditions. J. Evol. Equ. 6 (2006), 537-576. PDF for download.
  61. R. Schnaubelt: Exponential and polynomial dichotomies of operator semigroups in Banach spaces. Studia Math. 175 (2006), 121-138. PDF for download.
  62. J. Prüss, A. Rhandi, R. Schnaubelt: The domain of elliptic  operators on L^p(R^d) with unbounded drift coefficients. Houston J. Math. 32 (2006), 563-576. PDF for download.
  63. A. Batkai, K.-J. Engel, J. Prüss. R. Schnaubelt: Polynomial asymptotic stability of operator semigroups. Math. Nachr. 279 (2006), 1425-1440. PDF for download.
  64. G. Metafune, R. Schnaubelt: The domain of the Schrödinger operator -\Delta+x^2y^2. Note Mat. 25 (2005/06), 97-103. PDF for download.
  65. G. Metafune, D. Pallara, J. Prüss, R. Schnaubelt: L^p-theory for elliptic operators on R^n with singular coefficients. Z. Anal. Anwendungen 24 (2005), 497-521. PDF for download.
  66. D. Di Giorgio, A. Lunardi, R. Schnaubelt: Optimal regularity and Fredholm properties of abstract parabolic operators in L^p spaces on the real line. Proc. London Math. Soc. 91 (2005), 703-737. PDF for download.
  67. Y. Latushkin,  T. Randolph, R. Schnaubelt: Regularization and frequency-domain stability of well-posed control systems. Math. Control Signals Systems 17 (2005), 128-151. PDF for download.
  68. G. Metafune, J. Prüss, A. Rhandi, R. Schnaubelt: L^p-regularity for elliptic operators with unbounded coefficients. Adv. Differential Equations 10 (2005), 1131-1164. PDF for download.
  69. A. Batkai, R. Schnaubelt: Asymptotic behaviour of parabolic problems with  delays in the highest order derivatives. Semigroup Forum 69 (2004), 369-399. PDF for download.
  70. R. Schnaubelt: Parabolic evolution equations with asymptotically autonomous delay. Trans. Amer. Math. Soc. 356 (2004), 3517-3543. PDF for download.
  71. R. Schnaubelt: Asymptotic behaviour of parabolic nonautonomous evolution equations. In: M. Iannelli, R. Nagel, S. Piazzera (Eds.): "Functional Analytic Methods for Evolution Equations," Springer-Verlag, 2004, pp. 401-472. PDF for download.
  72. L. Maniar, R. Schnaubelt: Almost periodicity of inhomogeneous parabolic evolution equations.  In: G. Ruiz Goldstein, R. Nagel, S. Romanelli (Eds.): "Recent Contributions to Evolution Equations," Marcel Dekker, 2003, pp. 299-318. PDF for download.
  73. R. Schnaubelt: Feedbacks for non-autonomous regular linear systems. SIAM J. Control Optim. 41 (2002), 1141-1165. PDF for download.
  74. G. Metafune, J. Prüss, A. Rhandi, R. Schnaubelt: The domain of the Ornstein--Uhlenbeck operator  on an L^p-space with invariant measure. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) 1 (2002), 471-485. PDF for download.
  75. G. Gühring, F. Räbiger, R. Schnaubelt: A characteristic equation for nonautonomous partial functional differential equations. J. Differential Equations 181 (2002), 439-462. PDF for download.
  76. R. Schnaubelt: Well-posedness and asymptotic behaviour of non-autonomous linear evolution equations. In: A. Lorenzi, B. Ruf (Eds.): "Evolution Equations, Semigroups and Functional Analysis," Birkhäuser, 2002, pp. 311-338. PDF for download.
  77. G. Lumer, R. Schnaubelt: Time-dependent parabolic problems on non-cylindrical domains with inhomogeneous boundary conditions. J. Evol. Equ. 1 (2001), 291-309. PDF for download.
  78. J. Prüss. R. Schnaubelt: Solvability and maximal regularity of parabolic evolution equations with coeffcients continuous in time. J. Math. Anal. Appl. 256 (2001), 405-430. PDF for download.
  79. R. Schnaubelt: Asymptotically autonomous parabolic evolution equations. J. Evol. Equ. 1 (2001), 19-37. PDF for download.
  80. R. Schnaubelt: A sufficient condition for exponential dichotomy of parabolic evolution equations. In:  G. Lumer. L. Weis (Eds.): "Evolution Equations and their Applications in Physical and Life Sciences (Proceedings Bad Herrenalb, 1998)," Marcel Dekker, 2001, pp. 149-158. PDF for download.
  81. G. Metafune, A. Rhandi, R. Schnaubelt: Spectrum of the infinite-dimensional Laplacian.  Archiv Math. 75 (2000), 280-282. PDF for download.
  82. F. Räbiger, A. Rhandi, R. Schnaubelt, J. Voigt: Non-autonomous Miyadera perturbations. Differential Integral Equations 13 (2000), 341-368. PDF for download.
  83. R. Schnaubelt, J. Voigt: The non-autonomous Kato class. Arch. Math. 72 (1999), 454-460. PDF for download.
  84. G. Lumer, R. Schnaubelt: Local operator methods and time dependent parabolic equations on non-cylindrical domains. In: M. Demuth, E. Schrohe, B.-W. Schulze, J. Sjöstrand (Eds.): "Evolution Equations, Feshbach Resonances, Singular Hodge Theory," Mathematical Topics Vol. 16, Wiley, 1999, pp. 58-130. PDF for download.
  85. Y. Latushkin, R. Schnaubelt: The spectral mapping theorem for evolution semigroups on L^p associated with strongly continuous cocycles. Semigroup Forum 59 (1999), 404-414. PDF for download.
  86. Y. Latushkin, R. Schnaubelt: Evolution semigroups, translation algebras, and exponential dichotomy of cocycles. J. Differential Equations 159 (1999), 321-369. PDF for download.
  87. A. Rhandi, R. Schnaubelt: Asymptotic behaviour of a non-autonomous population equation with diffusion in L^1. Discrete  Contin. Dyn. Syst. 5 (1999), 663-683. PDF for download.
  88. R. Schnaubelt: Sufficient conditions for exponential stability and dichotomy of evolution equations. Forum Math. 11 (1999), 543-566. PDF for download.
  89. F. Räbiger, R. Schnaubelt: Absorption evolution families and exponential stability of  non-autonomous diffusion equations. Differential Integral Equations 12 (1999), 41-65. PDF for download.
  90. Nguyen Van Minh, F. Räbiger, R. Schnaubelt: Exponential stability, exponential expansiveness, and  exponential dichotomy of evolution equations on the half-line. Integral Equations Operator Theory 32 (1998), 332-353. PDF for download.
  91. Y. Latushkin, T. Randolph, R. Schnaubelt: Exponential dichotomy and mild solutions of nonautonomous equations in Banach spaces. J. Dynam. Differential Equations 10 (1998), 489-510. PDF for download.
  92. G. Nickel, R. Schnaubelt: An extension of Kato's stability condition for nonautonomous Cauchy problems. Taiwanese J. Math. 2 (1998), 483-496. PDF for download.
  93. F. Räbiger, A. Rhandi, R. Schnaubelt: Perturbation and an abstract characterization of evolution semigroups. J. Math. Anal. Appl. 198 (1996), 516-533. PDF for download.
  94. F. Räbiger R. Schnaubelt: The spectral mapping theorem for evolution semigroups on spaces of vector-valued functions. Semigroup Forum 52 (1996), 225-239. PDF for download.