Marek Bodnar's Home Page

Marek Bodnar, Ph.D.
Institute of Applied Mathematics and Mechanics
Department of Mathematics, Computer Science and Mechanics
Warsaw University
Banacha 2, 02-097 Warsaw, POLAND
Office room: 5630
Phone: (+48 22) 55-44-563
Fax: (+48 22) 55-44-300
e-mail: mbodnar@mimuw.edu.pl

Fields of interest

retarded functional differential equations, delay differential equations, large systems of interacting particles, mathematical modelling in biology.

delay differential equations — I am investigating systems of ordinary differential equation with time delays. As far I have been considering only constant delay. I was studying an integro-differential equations with delay;
large systems of interacting particles — I am looking for a macroscopic equation (partial differential equation or integro-differential equation) which can describe an evolution of a macroscopic density of the particle system

Scientific reserches are carried on together with Warsaw Biolmat Team.

Thesis

Ph.D. thesis: "Properties of the solution to DDE versus properties of the solution to ODE", tutor: Mirosław Lachowicz;
Master thesis: "Marchuk's Model with immune reactivity depending on time", tutor: Urszula Foryś;

Positions

1-st, October 2004 — now — assistant professor at Institute of Applied Mathematics and Mechanics, Warsaw University
1-st, October 2001 — 30-th, September 2004 — instructor at Institute of Applied Mathematics and Mechanics, Warsaw University
March 1st, 2002 — September 30th, 2003 — post-doc position at Faculty of Mathematic Complutense University in Madrid in the framework of 5th RTN Using Mathematical Modelling and Computer Simulation to Improve Cancer Therapy
September 1998 — September 2001 — Ph.D studies at Faculty of Mathematics, Informatics and Mechanics, Warsaw University

Conferences and Summer schools

June 1998 — V Mathematical Population Dynamics Conference, Zakopane (Poland), talk;
July — ECMI (European Consortium for Mathematics in Industry) 11-th ECMI Modeling Week, Milano (Italy)
September 1998 — IV National Conference Application of Mathematics in Biology and Medicine (KKZMBiM), Zwierzyniec, talk;
June 1999 — ESM (European Simulation and Modeling) Conference, Warsaw (Poland), talk;
June/July 1999 — TMBT (Theoretical and Mathematics in Biology and Medicine) Conference in Amsterdam (Holland), poster;
September 1999 — V KKZMBiM in Ustrzyki Górne, talk;
June 2000 — 1st Summer School and Scientific Workshop of RTN Using Mathematical Modelling and Computer Simulation to Improve Cancer Therapy, Propriano (Corse, France), talk;
1st ESMTB Euro Summer School Spatial Structures in Biology and Ecology: Models and Methods, Martina Franca (Italy), communication;
September 2001 — 2nd Summer School and Scientific Workshop of RTN Using Mathematical Modelling and Computer Simulation to Improve Cancer Therapy, Propriano (Corse, France), talk;
September 2001 — VII KKZMBiM, Zawoja (Poland), talk;
September 2002 — 2nd Summer School and Scientific Workshop of RTN Using Mathematical Modelling and Computer Simulation to Improve Cancer Therapy, Propriano (Corse, France), talk;
September 2003 — Linking mathematics and biology in cancer research, Magdeburg (Germany), talk;
September 2004 — X KKZMBiM, Jodłowy Dwór (Poland), talk;
May/June 2005 — Conference on Mathematical Models and Methods in Biology and Medicine, Będlewo (Poland), talk
October 2005, Workshop on Tumour Modelling, Szczyrk (Poland), talk
June 2006 — AIMS' Sixth International Conference on Dynamical Systems, Differential Equations and Applications, Poitires (France), talk
September 2006 — School and Workshop, From a Microscopic to a Macroscopic Description of Complex Systems, Będlewo (Poland), talk
September 2006 — XII KKZMBiM, Koninki (Poland), talk
July 2007 — Dynamics Days Europe 2007, Loughborough University (Great Britain), talk
September 2007 — XIII KKZMBiM, Serpelice nad Bugiem (Poland), talk
October 2007 — Workshop: From Genetics to Mathematics, Zbąszyń (Poland)

My publications:

Papers after referee process:

M. Bodnar, U. Foryś, A model of immune system with time-depended immune reactivity, Non. Anal. Th. Meth. Appl. DOI: 10.1016/j.na.2008.01.031
M. Bodnar, U. Foryś, Global stability and the Hopf bifurcation for some class of delay differential equation, Math. Methods Appl. Sci., 31, 10, (2008), 1197–1207, DOI: 10.1002/mma.965.
M. Bodnar, U. Foryś, Three types of simple DDE'S describing tumor growth, J. Biol. Syst., 15, 15, (2007), 453–471.
M. Bodnar, J.J.L. Velazquez, An integro-differential equation arising as a limit of individual cell-based models, J. Diff. Eqs., 222, 2, (2006), 341–380.
M. Bodnar, U. Foryś, A model of immune system with time depended immune reactivity, Proceedings of the XII National Conference Application of Mathematics in Biology and Medicine, Koninki, September 25–29, 2006, 19–24.
M. Bodnar, U. Foryś, Time delay in necrotic core formation, Math. Bio. Eng., 2, 3, (2005), 461–472.
M. Bodnar, J.J.L. Velazquez, Derivation of macroscopic equations for individual cell-based models: a formal approach, Math. Methods Appl. Sci., 28, 15 (2005), 1757–1779.
M. Bodnar, On the differences and similarities of the first order delay and ordinary differential equations, J. Math. Anal. Appl., 300, 1, (2004), 172–188.
M. Bodnar, U. Foryś, Time delay in a model of necrotic core formation. Proceedings of the X National Conference Application of Mathematics in Biology and Medicine, Jodłowy Dwór, September 21–25, 2004, 13–18.
U. Foryś, M. Bodnar, Time delays in regulatory apoptosis for solid avascular tumour, Math. Comput. Modelling, 37, 11, (2003), 1211–1220.
U. Foryś, M. Bodnar, Time delays in in proliferation process for solid avascular tumour, Math. Comput. Modelling, 37, 11, (2003), 1201–1209.
M. Bodnar, On Norm Conservation for Generalized Kinetic Population Models with Delay, Math. Comput. Modelling, 35,7-8 (2002), 765–778.
M. Bodnar, On some integro-differential models with delay in population dynamics, Proceedings of the VII National Conference Application of Mathematics in Biology and Medicine, Zawoja, September 25–28, 2001, 21–26.
M. Bodnar, On the nonnegativity of solutions of delay differential equations,Appl. Math. Lett., 13,6 (2000), 91–95.
M. Bodnar, U. Foryś, Behaviour of Marchuk's model depending on time delay, Intern. J. Appl. Math. Comput. Sci. 10, 1, (2000), 97–112.
M. Bodnar, U. Foryś, Periodic dynamics of the model of immune system, Appl. Math. (Warsaw), 27,1 (2000), 113–126.
M. Bodnar, U. Foryś, Forest-pest interaction dynamics, Proceedings of the V National Conference Application of Mathematics in Biology and Medicine, Ustrzyki Gorne, September 14–17, 1999, 15–20.
M. Bodnar, U. Foryś, A model of the immune system with stimulation depending on time, Proceedings of the IV National Conference Application of Mathematics in Biology and Medicine, Zwierzyniec, September 15–18, 1998, 12–17.

Papers without referee process:

M. Bodnar, D. Kuhnke, J. Pedersen, J. Ränäen, G. Haase, A mass reduction for the modulling machine, in Proceedings of 11th ECMI Modeling Week, Milan 1998.

Preprints:

M. Bodnar, U. Foryś, A model of the immune system with time-dependent immune reactivity, preprint of Institute of Applied Mathematics and Mechanics Warsaw University, RW 99-04 (52), February 1999.

Marek Bodnar's home page