Publications

EDITORIAL WORK


BOOKS

Fritz Gesteszy and Marcus Waurick

The Callias Index Formula Revisited 

Springer LNM 2157, 

201 (ix+192) pp, 2016. 

Rainer Picard, Des McGhee, Sascha Trostorff,  and Marcus Waurick

A Primer for a Secret Shortcut to PDEs of Mathematical Physics 

Birkhaeuser, Cham, 193 (x+183) pp, 2020.

Christian Seifert, Sascha Trostorff, and Marcus Waurick

Evolutionary Equations 

Birkhaeuser, Cham,  

329 (xii+317) pp, 2022, 

EDITED

Felix L. Schwenninger and Marcus Waurick (Eds)

Systems Theory and PDEs

Open Problems, Recent Results, and New Directions

Trends in Mathematics,  Birkhäuser Cham

205 (x+195) pp, 2024. 

JOURNAL ARTICLES

  1. Marcus Waurick
    Nonlocal H-convergence for topologically nontrivial domains
    Journal of Functional Analysis 288, 110710, 2025 arXiv

  2. Johanna Frohberg and Marcus Waurick
    State-dependent Delay Differential Equations on H1
    Journal of Differential Equations 410, 737–771, 2024 arXiv

  3. Rainer Picard, Sascha Trostorff, and Marcus Waurick
    Adjoints of sums of m-accretive operators and applications to non-autonomous evolutionary equations
    DAE Panel 2., https://doi.org/10.52825/dae-p.v2i.994, arXiv

  4. Nathanael Skrepek and Marcus Waurick
    Semi-uniform stabilization of anisotropic Maxwell's equations via boundary feedback on split boundary
    Journal of Differential Equations 394, 345-374 (2024). arXiv

  5. Krešimir Burazin, Marko Erceg, and Marcus Waurick
    Evolutionary Equations are G-compact
    Journal of Evolution Equations 24, No. 2, Paper No. 45, 20 p. (2024). arXiv

  6. Trostorff, S. and Waurick, M.
    Characterisation for Exponential Stability of port-Hamiltonian Systems
    Israel Journal of Mathematics accepted, 2024 arXiv

  7. Andreas Buchinger, Nathanael Skrepek and Marcus Waurick
    Weak Operator Continuity for Evolutionary Equations
    Pure and Applied Functional Analysis 9 (4), 963-990, 2024 arXiv

  8. Tomáš Dohnal, Mathias Ionescu-Tira, and Marcus Waurick
    Well-Posedness and Exponential Stability of Nonlinear Maxwell Equations for Dispersive Materials with Interface
    Journal of Differential Equations 383, 24-77 (2024). arXiv

  9. Picard, R; Trostorff, S.; Watson, B; and Waurick, M.
    A Structural Observation on port-Hamiltonian Systems
    SIAM J. Control Optim. 61, No. 2, 511-535, 2023. arXiv

  10. Diethelm, K; Kitzing, K.; Picard, R.; Siegmund, S.; Trostorff, S.; Waurick, M.
    A Hilbert space approach to fractional differential equations
    Journal of Dynamics and Differential Equations 34(1):481-504, 2022 arXiv

  11. Pauly, D. and Waurick, M.
    The Index of some mixed order Dirac-type operators and generalised Dirichlet-Neumann fields
    Mathematische Zeitschrift 301(2):1739-1819, 2022 arXiv

  12. Nicaise, S. and Waurick, M.
    Nonlocal homogenisation theory for curl-div-systems
    Mathematische Nachrichten 259(5):950-969, 2022 arXiv

  13. Neukamm, S., Varga, M. and Waurick, M.
    Two-scale homogenization of abstract linear time-dependent PDEs
    Asymptotic Analysis 125(3-4):247-287, 2021 arXiv

  14. Trostorff, S. and Waurick, M.
    Maximal Regularity for Non-Autonomous Evolutionary Equations.
    Integral Equations and Operator Theory no. 2, paper number 30, 37pp, 2021 arXiv

  15. Pauly, D.; Picard, R.; Trostorff, S. and Waurick, M.
    On a Class of Degenerate Abstract Parabolic Problems and Applications to Some Eddy Current Models
    Journal of Functional Analysis 280(7), paper number 108847, 45pp, 2021 arXiv

  16. Waurick, M. and S.-A. Wegner
    Dissipative extensions and port-Hamiltonian operators on networks
    Journal of Differential Equations 269(9): 6830--6874, 2020 arXiv

  17. Cooper, S. and Waurick, M.
    Fibre Homogenisation
    Journal of Functional Analysis 276(11):3363--3405, 2019 arXiv

  18. Trostorff, S. and Waurick, M.
    On Differential-Algebraic Equations in Infinite Dimensions
    Journal of Differential Equations 266(1): 526-561, 2019 arXiv

  19. Elst, A.F.M. ter; Gorden, G. and Waurick, M.
    The Dirichlet-to-Neumann operator for divergence form problems
    Annali di Matematica Pura ed Applicata https://arxiv.org/abs/1707.05734 arXiv

  20. Franz, S.; Trostorff, S. and Waurick, M.
    Numerical Methods for Changing Type Systems
    IMA Journal of Numerical Analysis 39(2): 1009-1038, 2019 arXiv

  21. Waurick, M.
    Homogenisation and the Weak Operator Topology
    Quantum Studies: Mathematics and Foundations 6(3) 375–396 2019 arXiv

  22. Waurick, M.
    Nonlocal H-convergence
    Calculus of Variations and Partial Differential Equations 57(6): Art. 159, 46 pp., 2018 arXiv

  23. Waurick, M. and Wegner, S.-A.
    Some remarks on the notions of boundary systems and boundary triple(t)s
    Mathematische Nachrichten 291(16): 2489-2497, 2018 arXiv

  24. Franz, S. and Waurick, M.
    Resolvent estimates and numerical implementation for the homogenisation of one-dimensional periodic mixed type problems
    Zeitschrift für Angewandte Mathematik und Mechanik 98(7): 1036-1294, 2018 arXiv

  25. Cherednichenko, K.; Waurick, M.
    Resolvent estimates in homogenisation of periodic problems of fractional elasticity
    Journal of Differential Equations 264(6): 3811–3835, 2018 arXiv

  26. Waurick, M.
    A Functional Analytic Perspective to the div-curl Lemma
    Journal of Operator Theory 80(1): 95-111, 2018 arXiv

  27. Franz, S.; Höhne, K.; Waurick, M.
    A solution decomposition for a singularly perturbed fourth-order problem
    Analysis 37(2):77--100, 2017 arXiv

  28. Garay, B.; Siegmund, S.; Trostorff, S.; Waurick, M.
    Some remarks on local activity and local passivity
    Internat. J. Bifur. Chaos Appl. Sci. Engrg. 27 (4), 1750057, 13 pp., 2017 arXiv

  29. Picard, R.; Trostorff, S.; Waurick, M.
    On Maximal Regularity for a Class of Evolutionary Equations
    Journal of Mathematical Analysis and Applications 449(2): 1368–1381, 2017 arXiv

  30. Süß, A.; Waurick, M.
    A Solution Theory for a General Class of SPDEs
    Stochastics and Partial Differential Equations: Analysis and Computations 5(2): 278-318, 2017 arXiv

  31. Mukhopadyay, S.; Picard, R.; Trostorff, S.; Waurick, M.
    A Note on a Two-Temperature Model in Linear Thermoelasticity.
    Math. Mech. Solids 22(5): 905-918, 2017 arXiv

  32. Picard, R.; Trostorff, S.; Waurick, M.
    On a Connection between the Maxwell System, the Extended Maxwell System, the Dirac Operator and Gravito-Electromagnetism.
    Math. Meth. Appl. Sci., 40(2): 415-434, 2017 arXiv

  33. Waurick, M.
    Stabilization via Homogenization
    Applied Mathematics Letters 60: 101-107, 2016 arXiv

  34. Waurick, M.
    On the homogenization of partial integro-differential-algebraic equations
    Operators and Matrices 10(2): 247-283, 2016 arXiv

  35. Mulholland, A. J.; Picard, R.; Trostorff, S.; Waurick, M.
    On well-posedness for some thermo-piezo-electric coupling models
    Math. Meth. Appl. Sci. 39(15): 4375-4384, 2016 arXiv

  36. Getto, P.; Waurick, M.
    A differential equation with state-dependent delay from cell population biology
    Journal of Differential Equations 260(7): 6176-6200, 2016 arXiv

  37. Picard, R.; Seidler, S; Trostorff, S.; Waurick, M.
    On Abstract grad-div Systems
    Journal of Differential Equations 260(6): 4888-4917, 2016 arXiv

  38. Seifert, C.; Waurick, M.
    Perturbations of positive semigroups on Lp-spaces.
    Positivity 20(2): 467-481, 2016 arXiv

  39. Mukhopadyay, S.; Picard, R.; Trostorff, S.; Waurick, M.
    On Some Models in Linear Thermo-Elasticity with Rational Material Laws.
    Mathematics and Mechanics of Solids 21(9): 1149-1163, 2016 arXiv

  40. Picard, R.; Trostorff, S.; Waurick, M.
    On a Comprehensive Class of Linear Control Problems.
    IMA Journal of Mathematical Control and Information 33 (2): 257-291, 2016 arXiv

  41. Schubert, C.; Seifert, C.; Voigt, J.; Waurick, M
    Boundary systems and (skew-)self-adjoint operators on infinite metric graphs
    Mathematische Nachrichten 288(14-15): 1776-1785, 2015 arXiv

  42. Waurick, M.
    A note on causality in Banach spaces.
    Indagationes Mathematicae 26(2): 404-412, 2015 arXiv

  43. Picard, R.; Trostorff, S.; Waurick, M.
    On Evolutionary Equations with Material Laws Containing Fractional Integrals
    Math. Meth. Appl. Sci. 38(15): 3141-3154, 2015 arXiv

  44. Picard, R.; Trostorff, S.; Waurick, M.
    On Some Models for Elastic Solids with Micro-Structure
    Zeitschrift für Angewandte Mathematik und Mechanik 95(7): 664-689, 2015 arXiv

  45. Waurick, M.
    On Non-Autonomous Integro-Differential-Algebraic Evolutionary Problems.
    Mathematical Methods in the Applied Sciences 38(4): 665-676, 2015 arXiv

  46. Waurick, M.
    G-convergence of linear differential equations
    Journal of Analysis and its Applications 33(4): 385-415, 2014 arXiv

  47. Waurick, M.
    Homogenization in fractional elasticity
    SIAM J. Math. Anal. 46(2): 1551-1576, 2014 arXiv

  48. Trostorff, S; Waurick M.
    A note on elliptic type boundary value problems with maximal monotone relations
    Mathematische Nachrichten 287(13): 1545-1558, 2014 arXiv

  49. Kalauch, A.; Picard, R.; Siegmund, S.; Trostorff, S.; Waurick, M.
    A Hilbert Space Perspective on Ordinary Differential Equations with Memory Term
    Journal of Dynamics and Differential Equations 26(2):369-399, 2014 arXiv

  50. Picard, R.; Trostorff, S.; Waurick, M.
    A Functional Analytic Perspective to Delay Differential Equations
    Oper. Matrices 8(1): 217-236, 2014 arXiv

  51. Picard, R.; Trostorff, S.; Waurick, M.
    On a Class of Boundary Control Problems
    Oper. Matrices 8(1): 185-204, 2014 arXiv

  52. Picard, R.; Trostorff, S.; Waurick, M.; Wehowski, M.
    On Non-Autonomous Evolutionary Problems
    Journal of Evolution Equations 13:751-776, 2013 arXiv

  53. Waurick, M.
    Homogenization of a class of linear partial differential equations
    Asymptotic Analysis 82: 271-294, 2013.

  54. Pannier, S.; Waurick M.; Graf, W.; Kaliske, M.
    Solutions to problems with imprecise data - An engineering perspective to generalized uncertainty models
    Mechanical Systems and Signal Processing 37 (1-2):105-120, 2013

  55. Waurick, M.
    A Hilbert Space Approach to Homogenization of Linear Ordinary Differential Equations Including Delay and Memory Terms
    Mathematical Methods in the Applied Sciences 35(9): 1067-1077,2012

BOOK CHAPTERS / PROCEEDINGS

  1. Waurick, M. and Zwart, H.
    Asymptotic Stability of port-Hamiltonian Systems
    Systems theory and PDEs -- Open Problems, Recent Results, and New Directions arXiv

  2. Franz, S. and Waurick, M.
    Homogenisation of parabolic/hyperbolic media
    Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2018 2020 arXiv

  3. Kitzing, K.; Picard, R.; Siegmund, S.; Trostorff, S.; Waurick, M.
    A Hilbert space approach to difference equations
    Difference equations, discrete dynamical systems and applications 285–307, Springer Proc. Math. Stat., 287, Springer, Cham, 2019. arXiv

  4. Waurick, M.
    Continuous dependence on the coefficients for a class of non-autonomous evolutionary equations
    Maxwell’s Equations Analysis and Numerics Series: Radon Series on Computational and Applied Mathematics 24, 2019. arXiv

  5. Picard, R.; Trostorff, S. and Waurick, M.
    On the Well-posedness of a Class of Non-Autonomous SPDEs: An Operator-Theoretical Perspective
    GAMM-Mitteilungen 41(4): e201800014, Applied Operator Theory ‐ Part II, 2018 arXiv

  6. Waurick, M.
    On operator norm convergence in time‐dependent homogenisation problems
    PAMM 18, doi:10.1002/pamm.201800009, 2018

  7. Trostorff, S. and Waurick, M.
    On Higher Index Differential-Algebraic-Equations in Infinite Dimensions
    The diversity and beauty of applied operator theory Oper. Theory Adv. Appl., 268, 477-486, Birkhäuser/Springer, Cham, 2018 arXiv

  8. Waurick, M.
    G-convergence and the weak operator topology
    PAMM 16, 883-884, 2016

  9. Picard, R.; Seidler, S.; Trostorff, S.; Waurick, M.
    On a Particular Construction of Skew-Selfadjoint Operator Matrices
    PAMM 15, 695-696, 2015

  10. Picard, R.; Trostorff, S.; Waurick, M.
    Well-posedness via Monotonicity. An Overview.
    Operator semigroups meet complex analysis, harmonic analysis and mathematical physics Oper. Theory Adv. Appl., 250:397-452, Springer, Cham, 2015 arXiv

  11. McGhee, D.; Picard, R.; Trostorff, S.; Waurick, M.
    Partial Differential Equations
    Mathematical Tools for Physicists 2nd Edition, Grinfeld (Editor), Wiley-VCH, 2014

  12. McGhee, D.; Picard, R.; Trostorff, S.; Waurick, M.
    Mathematical Transformations
    Mathematical Tools for Physicists 2nd Edition, Grinfeld (Editor), Wiley-VCH, 2014

  13. Waurick, M.
    A note on causality in reflexive Banach spaces
    PAMM 14, 987-988, 2014

  14. Waurick, M.
    Homogenization in Fractional Elasticity - One spatial dimension
    PAMM 13, 521-522, 2013

  15. Picard, R.; Trostorff, S.; Waurick, M.
    A note on a class of conservative, well-posed linear control systems
    Progress in partial differential equations (M. Reissig, M. Ruzhansky eds.) Springer Proceedings in Mathematics and Statistics, 44: 261-286 Springer, Cham, 2013.

  16. Picard, R.; Trostorff, S.; Waurick, M.
    Well-posedness and Conservativity for Linear Control Systems (Part 1)
    PAMM 12, 777-778, 2012

  17. Picard, R.; Trostorff, S.; Waurick, M.
    Well-posedness and Conservativity for Linear Control Systems (Part 2)
    PAMM 12, 779-780, 2012

  18. Waurick, M.
    On the well-posedness of evolutionary equations on infinite graphs
    Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations. Operator Theory: Advances and Applications, Birkhaeuser, 221: 653-666, 2012. arXiv

  19. Waurick, M.; Kaliske, M.
    A Note on Homogenization of Ordinary Differential Equations with Delay Term
    PAMM 11, 889-890, 2011

PREPRINTS

  1. Bernhard Aigner and Marcus Waurick
    A quick guide to ordinary state-dependent delay differential equations
    arXiv

  2. Sahiba Arora, Felix Schwenninger, Ingrid Vukusic, and Marcus Waurick
    A universal example for quantitative semi-uniform stability
    arXiv

  3. Andreas Buchinger, Sebastian Franz, Nathanael Skrepek, and Marcus Waurick
    Homogenisation for Maxwell and Friends
    arXiv

  4. Shane Cooper, Imane Essadeq and Marcus Waurick
    Fibre homogenisation for time-dependent problems
    arXiv

  5. Bernhard Aigner and Marcus Waurick
    A simple way to well-posedness in H1 of a delay differential equation from cell biology
    arXiv

  6. Krešimir Burazin, Marco Erceg, and Marcus Waurick
    G-convergence of Friedrichs Systems Revisited
    arXiv

  7. Waurick, M.
    Homogenisation of Laminated Metamaterials and the Inner Spectrum
    arXiv

THESES



  • Habilitation Thesis On the continuous dependence on the coefficients of evolutionary equations arXiv.
    TU Dresden (2016)
  • PhD Thesis Limiting Processes in Evolutionary Equations - A Hilbert Space Approach to Homogenization Link 
    TU Dresden (2011)
  • Diploma Thesis Transport und Wellenausbreitung auf Pseudographen 
    TU Dresden (2009)


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