| Monographs (since 1994)
|
| M. Lachowicz, Asymptotic Analysis of Nonlinear Kinetic Equations: The Hydrodynamic Limit, in Lecture Notes on the Mathematical Theory of the Boltzmann Equation, World Scientific, Singapore 1995, 65-148. |
| L. Arlotti, N. Bellomo, E. De Angelis, M. Lachowicz, Generalized Kinetic Models in Applied Sciences, World Sci., New Jersey 2003. |
| M. Lachowicz, Links Between Microscopic and Macroscopic Descriptions, in Multiscale Problems in the Life Sciences. From Microscopic to Macroscopic, Eds. V. Capasso, M. Lachowicz, Lecture Notes in Mathematics 1940, Springer, 2008, 201-268. |
| M. Lachowicz, J. Miękisz (Eds.), From Genetics to Mathematics, World Sci., New Jersey 2009. |
| Special Issue
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| M. Kimmel, M. Lachowicz, A. Świerniak (Eds.), International Journal of Applied Mathematics and Computer Science, Vol. 13, No. 3, 2003, Cancer Growth and Progression, Mathematical Problems and Computer Simulations. |
| Publications (since 1994)
|
| M. Lachowicz, Stochastic differential equations for the kinetic and hydrodynamic equations, Nonlinear Dyn., 5, 1994, 393-399. |
| N. Bellomo, M. Esteban, M. Lachowicz, Nonlinear kinetic equations with dissipative collisions, Appl. Math. Lett., 8, (5), 1995, 47-52. |
| L. Arlotti, M. Lachowicz, Qualitative analysis of an equation modelling tumor-host dynamics, Math. Comput. Model., 23, (6), 1996, 11-29. |
| L. Arlotti, M. Lachowicz, On the hydrodynamic limit for quantum kinetic equations, Compt. Rend. Acad. Sci. Paris, 323, S. I, 1996, 101-106. |
| L. Arlotti, M. Lachowicz, Euler and Navier-Stokes limits of the Uehling-Uhlenbeck quantum kinetic equations, J. Math. Phys., 38, 1997, 3571-3588. |
| N. Bellomo, M. Lachowicz, J. Polewczak, On a mathematical model in theoretical immunology, Appl. Math. Lett., 10, (4), 1997, 53-58. |
| M. Lachowicz, From kinetic to Navier-Stokes-type equations, Appl. Math. Lett., 10, (5), 1997, 19-23. |
| M. Lachowicz, Hydrodynamic limits of stochastic kinetic equations I, ARI, 50, (2), 1997, 131-140. |
| M. Lachowicz, On the hydrodynamic limit of the Enskog equation, Publ. Res. Inst. Math. Sci., 34, 1998, 191-210. |
| M. Lachowicz, Nonlocal coagulation and fragmentation, Proceedings of the Fifth National Conference on Application of Mathematics in Biology and Medicine, Ustrzyki G., September 14-17, 1999, 93-98. |
| L. Arlotti, N. Bellomo, M. Lachowicz, Kinetic equations modelling population dynamics, Transport Theory Statist. Physics, 29, (1-2), 2000, 125-139. |
| M. Lachowicz, D. Wrzosek, A nonlocal coagulation-fragmentation model, Appl. Math. (Warsaw), 27, (1), 2000, 45-66. |
| S. Jagodziński, M. Lachowicz, Incompressible Navier-Stokes limit for the Enskog equation, Appl. Math. Lett., 13, 2000, 107-111. |
| M. Lachowicz, Hydrodynamic limits of some kinetic equations, First RIMS Workshop on Mathematical Analysis in Fluid and Gas Dynamics, Kyoto, July 12-14, 1999, Eds. A. Matsumura & S. Kawashima, Surikaisekikenkyusho Kokyuroku N. 1146, 2000, RIMS Kyoto Univ., 121-143. |
| M. Lachowicz, Is the linearized Boltzmann-Enskog operator dissipative?, Appl. Math. Lett., 14, 2001, 291-295. |
| M. Lachowicz, Competition tumor - immune system, Proceedings of the Sixth National Conference on Application of Mathematics in Biology and Medicine, Zawoja, September 12-15, 2000, 89-93. |
| L. Arlotti, A. Gamba, M. Lachowicz, A kinetic model of tumor-immune system cellular interactions, J. Theoret. Medicine, 4 (1), 2002, 39-50. |
| M. Lachowicz, D. Wrzosek, Nonlocal bilinear equations. Equilibrium solutions and diffusive limit, Math. Models Methods Appl. Sci., 11, no. 8, 2001, 1393-1409. |
| J. Banasiak, M. Lachowicz, Chaos for a class of linear kinetic models, Compt. Rend. Acad. Sci. Paris, 329, S. IIb, 2001, 439-444. |
| M. Lachowicz, When topology meets medicine, Proceedings of the Seventh National Conference on Application of Mathematics in Biology and Medicine, Zawoja, September 25-28, 2001, 117-122. |
| J. Banasiak, M. Lachowicz, Topological chaos for birth-and-death-type models with proliferation, Math. Models Methods Appl. Sci., 12, 6, 2002, 755-775. |
| M. Lachowicz, From microscopic to macroscopic description for generalized kinetic models, Math. Models Methods Appl. Sci., 12, 7, 2002, 985-1005. |
| J. Banasiak, M. Lachowicz, Chaotic linear dynamical systems with applications, The Proceedings of the 2nd International Conference on Semigroups of Operators: Theory and Applications SOTA 2, Rio de Janeiro, 10-14 September 2001, Eds. C. Kubrusly, N. Levan, and M. da Silveira, Optimization Software, Los Angeles, 2002, 32-44. |
| J. Banasiak, M. Lachowicz & M. Moszynski, Topological chaos: When topology meets medicine, Appl. Math. Lett., 16, 2003, 303-308. |
| M. Lachowicz, Describing competitive systems at the level of interacting individuals, Proceedings of the Eighth National Conference on Application of Mathematics in Biology and Medicine, Lajs, September 24-27, 2002, 95-100. |
| M. Lachowicz, On bilinear kinetic equations. Between micro and macro description of biological populations, Banach Center Publ., 63, 2004, 217-230. |
| M. Lachowicz, Ph. Laurencot, & D. Wrzosek, On the Oort-Hulst-Safranov coagulation equation and its relation to the Smoluchowski equation, SIAM J. Math. Anal., 34, 6, 2003, 1399-1421. |
| M. Lachowicz, From microscopic to macroscopic descriptions of complex systems, Compt. Rend. Acad. Sci. Paris, S�ie IIb, 2003, 331, 2003, 733-738. |
| S. Jagodziński, M. Lachowicz, On two incompressible hydrodynamic limits of the Boltzmann-Enskog equation I: Formal derivation, Transport Theory Statist. Physics 33, 2, 2004, 157-181. |
| M. Kolev, E. Kozłowska, M. Lachowicz, A mathematical model for single cell cancer - immune system dynamics, Math. Comput. Model., 41, 10, 2005, 1083-1095. |
| L. Arlotti, A. Deutsch, M. Lachowicz, On a discrete Boltzmann-type model of swarming, Math. Comput. Model., 41, 10, 2005, 1193-1201. |
| M. Lachowicz, General population systems. Macroscopic limit of a class of stochastic semigroups, J. Math. Anal. Appl., 307/2, 2005, 585-605. |
| M. Lachowicz, Stochastic semigroups and coagulation equations, Ukrainian Math. J., 57, 6, 2005, 770-777. |
| M. Lachowicz, Micro and meso scales of description corresponding to a model of tissue invasion by solid tumours, Math. Models Methods Appl. Sci., 15, 2005, 1667-1683. |
| S. Jagodziński, M. Lachowicz, On two incompressible hydrodynamic limits of the Boltzmann-Enskog equation II: A rigorous result, Transport Theory Statist. Physics 34, 2005, 447-474. |
| J. Banasiak, M. Lachowicz, M. Moszyński, Semigroups for generalized birth-and-death equation in lp spaces, Semigroup Forum 73, 2006, 175-193. |
| J. Banasiak, M. Lachowicz, M. Moszyński, Chaotic behavior of semigroups related to the process of gene amplification-deamplification with cell proliferation, Math. Biosci., 206, 2007, 200-215 |
| J. Banasiak, M. Lachowicz, Around the Kato generation theorem for semigroups, Studia Math. 179, 3, 2007, 217-238 |
| M. Lachowicz, Towards microscopic and nonlocal models of tumour invasion of tissue, Eds. N. Bellomo, M. Chaplain, E. De Angelis, Birkhauser, Boston 2008, 49-63 |
| Z. Szymańska, C. Morales Rodrigo, M. Lachowicz, M. Chaplain, Mathematical modelling of cancer invasion of tissue: The role and effect of nonlocal interactions, Math. Models Methods Appl. Sci. 19 (2), 2009, 257-281 |
| M. Chaplain, M. Lachowicz, Z. Szymańska, D. Wrzosek, Mathematical modelling of cancer invasion: The importance of cell-cell adhesion and cell-matrix adhesion, Math. Models Methods Appl. Sci. 24 (4), 2011, 719-743 |
| M. Lachowicz, Microscopic, mesoscopic and macroscopic descriptions of complex systems, Prob. Engin. Mech., 26 (2011), 54-60, 26 (1), 2011, 54-60 |
| J. Banasiak, M. Lachowicz, Multiscale approach in mathematical biology, Phys. Life Reviews 8 (1), 2011, 19-20 |
| M. Lachowicz, Individually-based Markov processes modeling nonlinear systems in mathematical biology, Nonlinear Analysis Real World Appl., 12, 4, 2011, 2396-2407 (doi:10.1016/j.nonrwa.2011.02.014) |
| L. Arlotti, E. De Angelis, L. Fermo, M. Lachowicz, N. Bellomo, On a Class of Integro-Differential Equations Modeling Complex Systems with Nonlinear Interactions, Appl. Math. Letters 25 (2012), 490-495 |
| Papers in Polish
|
| M. Lachowicz & D. Wrzosek, Matematyczne modele zjawisk przyrodniczych, Matematyka, Społeczeństwo, Nauczanie, OKM, 15, 1995, 4 - 15. |
| M. Lachowicz, Między mikroświatem a makroświatem - Analiza asymptotyczna, Wiadom. Mat., 32, s. II, 1996, 37-49. |
| M. Lachowicz, Matematyka chaosu, Matematyka, Społeczeństwo, Nauczanie, OKM, 22, 1999, 21-28. |
| M. Lachowicz, Modele matematyczne w biologii, Matematyka Stosowana - Matematyka dla społeczeństwa, 1, 42, 2000, 3-34. |
| M. Lachowicz, Dziwny atraktor Lorenza, Delta, 12(355), 2003, 1. |
| Entry in Encyclopedia
|
| M. Lachowicz, Model matematyczny, Wielka Encyklopedia PWN, tom 17. |
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