Ryszard Rudnicki, Professor

Ph.D.: 1986 Silesian University, habilitation: 1993 Silesian University, professor: 2001 Institute of Mathematics PAS.

Professional interests:

  1. Mathematical models of populations dynamics,
  2. Asymptotic properties of partial differential equations,
  3. Asymptotic behaviour of semigroups of positive operators,
  4. Theory of Markov operators and their applications to transport equations,
  5. Chaotic and ergodic properties of infinite-dimensional dynamical systems.
  6. Markov processes - limit theorems and properties of paths.

List of selected publications (till 2005):

  1. Invariant measures for the flow of a first order partial differential equation, Ergodic Theory Dynamical Systems, 5 (1985), 437-443.
  2. Strong ergodic properties of a first-order partial differential equation, J. Math. Anal. Appl., 133 (1988), 14-26.
  3. Asymptotical stability in L1 of parabolic equations, J. Diff. Eq., 102 (1993), 391-401.
  4. with M. C. Mackey, Asymptotic similarity and Malthusian growth in autonomous and nonautonomous populations, J. Math. Anal. Appl., 187 (1994), 548-566.
  5. with M. C. Mackey, Global stability in a delayed partial differential equation describing cellular replication, J. Math. Biol., 33 (1994), 89-109.
  6. with K. Łoskot, Limit theorems for stochastically perturbed dynamical systems, J. App. Prob., 32 (1995), 459-469.
  7. On asymptotic stability and sweeping for Markov operators, Bull. Polish Acad. Sci. Math., 43 (1995), 245-262.
  8. with J. Łuczka, Randomly flashing diffusion: asymptotic properties, J. Statis. Phys. 83 (1996), 1149-1164.
  9. with K. Pichór, Stability of Markov semigroups and applications to parabolic systems, J. Math. Anal. Appl., 215 (1997), 56-74.
  10. with K. Pichór, Asymptotic behaviour of Markov semigroups and applications to transport equations, Bull. Polish Acad. Sci. Math., 45 (1997), 379-397.
  11. with M. C. Mackey, A new criterion for global stability of cell simultaneous cell replication and maturation processes, J. Math. Biol., 38 (1999), 195-219.
  12. with K. Pichór, Markov semigroups and stability of the cell maturity distribution, J. Biol. Systems 8 (2000), 69-94.
  13. with K. Pichór, Continuous Markov semigroups and stability of transport equations, J. Math. Anal. Appl., 249 (2000), 668-685.
  14. Pointwise dimensions and Renyi dimensions, Proc. Amer. Math. Soc., 130 (2002), 1981-1982.
  15. Long-time behaviour of a stochastic prey-predator model, Stoch. Processes Appl., 108 (2003), 93-107.
  16. with O. Arino, Phytoplankton dynamics, Comptes Rendus Biologies, 327 (2004), 961-969.
Publications from the last three years:
  1. with P. Hanggi and J. Łuczka, The diffusion in the quantum Smoluchowski equation, Physica A, 351 (2005), 60-68.
  2. with W.T. Mocek, E.O. Voit, Approximation of delays in biochemical systems, Mathematical Biosciences 198 (2005), 190-216.
  3. with R. Wieczorek, Fragmentation -- coagulation models of phytoplankton, Bull. Pol. Acad. Sci. Math. 54 (2006), 175-191.
  4. with K. Nishimura and J. Stachurski, Stochastic optimal growth with nonconvexities, J. Math. Economics 42 (2006), 74-96.
  5. with J. Tiuryn and D. Wójtowicz, A model for the evolution of paralog families in genomes, J. Math. Biology 53 (2006), 759-770.
  6. with R. Wieczorek, Phytoplankton dynamics: from the behaviour of cells to a transport equation, Mathematical Modelling of Natural Phenomena 1 (2006), 83-100.
  7. with K. Pichór, Influence of stochastic perturbation on prey-predator systems, Mathematical Biosciences 206 (2007), 108-119.
  8. with A. Bobrowski, T. Lipniacki, K. Pichór, Asymptotic behavior of distributions of mRNA and protein levels in a model of stochastic gene expression, J. Math. Anal. Appl.,333 (2007), 753-769.
  9. with J. Myjak, On the information dimensions, Bolletino UMI 10 (2007), 357-364.
  10. with J. Tiuryn and D. Wójtowicz, A model of evolution of small paralog families in genomes, Mathematical Models and Methods in Applied Sciences 17 (2007), 933-955.