Research interests

functional analysis, operator theory, operator semigroups, evolution equations, control theory;
dynamical networks, conservation laws;
linear algebra, spectral properties, matrix groups;


 
ORCID iD iconorcid.org/0000-0003-1784-3090
  arXiv,   MathSciNet,   zbMATH,   Cobiss

Projects

COST Action CA18232 - Mathematical models for interacting dynamics on networks

Books

  A. Bátkai, M. Kramar Fijavž, A. Rhandi, Positive Operator Semigroups: from Finite to Infinite Dimensions, Birkhauser-Verlag, Basel, 2017.


Papers

  1. C. Budde, M. Kramar Fijavž, Well-posedness of non-autonomous transport equation on metric graphs, Semigroup Forum (2024), arXiv:2206.02540
  2. E. Kramar, M. Kramar Fijavž, A generalization of Kleinecke-Shirokov theorem for matrices, Operators and Matrices 17, 1 (2023), 51-55.
  3. K.-J. Engel, M. Kramar Fijavž, Flows on Metric Graphs with General Boundary Conditions, J. Math. Anal. Appl 513 (2022), 126214. arXiv:2110.08553
  4. C. Budde, M. Kramar Fijavž, Bi-continuous semigroups for flows in infinite networks, Networks and Heterogeneous Media 16 (2021), 553-567. arXiv:1901.10292
  5. M. Kramar Fijavž, D. Mugnolo, S. Nicaise, Dynamic Transmission Conditions for Linear Hyperbolic Systems on Networks, J. Evol. Equ. 21 (2021), 3639-3673. arXiv:2007.08298
  6. M. Kramar Fijavž, D. Mugnolo, S. Nicaise, Linear Hyperbolic Systems on Networks: well-posedness and qualitative properties, ESAIM: COCV 27, 7 (2021). arXiv:2003.08281
  7. M. Kramar Fijavž, A. Puchalska, Semigroups for dynamical processes on metric graphs, Phil. Trans. R. Soc. A. 378: 20190619 (2020). arXiv:2006.03123
  8. M. Kaplin, M. Kramar Fijavž, Generation of relatively uniformly continuous Semigroups on Vector Lattices, Anal Math 46, 293-322 (2020). arXiv:1809.11026 SharedIt
  9. J. Zevnik, M. Kramar Fijavž, D. Kozelj, Generalized normalized cut and spanning trees for water distribution network partitioning, J. of Water Resources Planning and Management, Vol. 145, Issue 10 (2019), 1-12.
  10. K.-J. Engel, M. Kramar Fijavž, Waves and Diffusion on Metric Graphs with General Vertex Conditions, Evol. Equ. Control Theory, 8 (2019), 633-661. arXiv:1712.03030
  11. J. Zevnik, M. Kramar Fijavž, D. Kozelj, Učinkovita particija vodovodnih omrežij na merilna območja z uporabo teorije grafov / Efficient partitioning of water distribution networks using a graph-theoretical approach (slovene), Acta hydrotechnica 54 (2018), 35-50.
  12. D. Kozelj, M. Gorjup, M. Kramar Fijavž, Uporaba teorije grafov za zasnovo merilnih območij v vodovodnem omrežju / An application of spectral graph partition for designing district metered areas in water supply networks (slovene), Acta hydrotechnica 53 (2017), 81-96.
  13. N. Bezak, S. Rusjan, M. Kramar Fijavž, M.Mikoš, M. Šraj, Estimation of Suspended Sediment Loads Using Copula Functions, Water 9 (2017), no. 8: 628.
  14. K.-J. Engel, M. Kramar Fijavž, Exact and Positive Controllability of Boundary Control Systems , J. Networks Heterogeneous Media, 12 (2017), 319-337. arXiv:1610.00954
  15. B. Andreianov, M. Kramar Fijavž, A. Peperko, E. Sikolya, Erratum to: Semigroups of max-plus linear operators , Semigroup Forum, 94 (2017), 477-479. arXiv:1411.5142
  16. M. Kramar Fijavž, A. Peperko, E. Sikolya, Semigroups of max-plus linear operators , Semigroup Forum, 94 (2017), 463-476. arXiv:1411.5142
  17. I. Strnad, M. Kramar Fijavž, M. Žura, Numerical optimal control method for shockwaves reduction at stationary bottlenecks, Journal of advanced transportation 50 (2016), 841-856.
  18. M. Kramar Fijavž, Kako išče Google? / How Google works? (slovene), Obzornik Mat. Fiz. 61 (2014), 121-131.
  19. W. Arendt, D. Dier, M. Kramar Fijavž, Diffusion in networks with time-dependent transmission conditions , Appl. Math. Optim. 69 (2014), 315-336. arXiv:1303.4951
  20. B. Dorn, F. Bayazit, M. Kramar Fijavž, Asymptotic periodicity of flows in time-depending networks, J. Networks Heterogeneous Media, 8 (2013), 843?855. arXiv:1302.4196
  21. M. Kramar Fijavž, M. Lakner, M. Škapin Rugelj, Equal-area method for scalar conservation laws, The ANZIAM Journal 53 (2012), 156-170. arXiv:1002.3260
  22. Semigroups Working Group at Law'08, Kranjska Gora, Semigroups of operators with nonnegative diagonals, Linear Algebra Appl. 433 (2010), 2080-2087.
  23. K.-J. Engel, M. Kramar Fijavž, B. Klöss, R. Nagel, E. Sikolya, Maximal controllability for boundary control problems, Appl. Math. Optim. 62 (2010), 205-227.
  24. B. Dorn, M. Kramar Fijavž, R. Nagel, A. Radl, The semigroup approach to flows in networks, Physica D: Nonlinear Phenomena 239 (2010), 1416-1421.
  25. K.-J. Engel, M. Kramar Fijavž, R. Nagel, E. Sikolya, Vertex control of flows in networks, J. Networks Heterogeneous Media 3 (2008), 709?722.
  26. M. Kramar Fijavž, D. Mugnolo, E. Sikolya, Variational and semigroup methods for waves and diffusion in networks , Appl. Math. Optim. 55 (2007), 219?240. arXiv:1209.1495
  27. Semitransitivity Working Group at LAW'05, Bled, Semitransitive subspaces of matrices, Electron. j. linear algebra (On line) 15 (2006), 225-238.
  28. M. Kramar, Representations of p-groups with submultiplicative spectra, Linear and Multilinear Algebra 54 (2006), 313-320.
  29. M. Kramar, The structure of irreducible matrix groups with submultiplicative spectrum, Linear and Multilinear Algebra 53 (2005), 13-25.
  30. M. Kramar, E. Sikolya, Spectral properties and asymptotic periodicity of flows on networks, Math Z. 249 (2005), 139-162.
  31. M. Kramar, Irreducible groups with submultiplicative spectrum, Lin. Alg. Appl. 378 (2004), 273-282.
  32. M. Kramar, D. Mugnolo, R. Nagel, Semigroups for initial-boundary value problems, Progress in Nonlinear Differential Equations, Vol. 55, 275-292, Birkhauser Verlag 2003.
  33. M. Kramar, D. Mugnolo, R. Nagel, Theory and applications of one-sided coupled operator matrices, Conf. Semin. Mat. Univ. Bari, 283 (2002), 1-29.