Monographs (since 1994)
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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. |
J. Banasiak, M. Lachowicz, Methods of small parameter in mathematical biology, Birkhäuser, Boston 2014. |
Editor
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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. |
M. Lachowicz, J. Miękisz (Eds.), From Genetics to Mathematics, World Sci., New Jersey 2009. |
J. Banasiak, A. Bobrowski, M. Lachowicz (Eds.), Semigroups of Operators - Theory and Applications SOTA 2013, Springer Proceedings in Mathematics and Statistics 113, 2015. |
A. Friedman, M. Lachowicz, U. Ledzewicz, M.J. Piotrowska, Z. Szymańska (Eds.), Micro and Macro Systems in Life Sciences, Mathematical Biosciences and Engineering 14(1), 2017. |
R. Anguelov, M. Lachowicz (Eds.), Mathematical Methods and Models in Biosciences, International Conference BIOMATH 2017, Kruger Park, Biomath Forum Sofia 2018. |
J. Banasiak, A. Bobrowski, M. Lachowicz, Y. Tomilov (Eds.), Semigroups of Operators - Theory and Applications SOTA 2018, Springer Proceedings in Mathematics and Statistics 325, 2020. |
J. Banasiak, M. Lachowicz (Eds.), Biomathematics (BIOMATH 2019), Mathematical Methods in the Applied Sciences, December 2020, 43, 18, 10355-10710.
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Publications (since 1994)
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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, Birkhäuser, 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, 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 |
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 |
M. Lachowicz, A. Quartarone, A general framework for modeling tumor-immune system competition at the mesoscopic level, Appl. Math. Letters 25, 2012, 2118-2122 |
J. Banasiak, E. Kimba Phongi, M. Lachowicz, A singularly perturbed SIS model with age structure, Math. Biosci. Engineering 10, 2013, 499-521 |
J. Banasiak, M. Lachowicz, On a macroscopic limit of a kinetic model of alignment, Math. Models Methods Appl. Sci. 23, 2013, 2647-2670 |
M. Lachowicz, T. Ryabukha, Equilibrium solutions for microscopic stochastic systems in population dynamics, Math. Biosci. Engineering 10, 2013, 777-786 |
M. Lachowicz, A. Quartarone, T. Ryabukha, Stability of solutions of kinetic equations corresponding to the replicator dynamics, Kinetic Related Models 7 (1), 2014, 109-119 |
M. Dolfin, M. Lachowicz, Modeling altruism and selfishness in welfare dynamics: The role of nonlinear interactions, Math. Models Methods Appl. Sci. 24 (12), 2014, 2361-2381 |
M. Dolfin, M. Lachowicz, Modeling DNA thermal denaturation at the mesoscopic level, Discrete Contin. Dyn. Syst. Ser. B 19 (8), 2014, 2469-2482 |
M. Dolfin, M. Lachowicz, Z. Szymańska, A general framework for multiscale modeling of tumor - immune system interactions, In Mathematical Oncology, Eds. A. d'Onofrio, A. Gandolfi, Birkhäuser, Boston 2014, 151-180 |
Z. Szymańska, M. Parisot, M. Lachowicz, Mathematical modeling of the intracellular protein dynamics: The importance of active transport along microtubules, J. Theoret. Biol. 363, 2014, 118-128 |
M. Lachowicz, Z. Szymańska, Nonlocal models of biological phenomena, Phys. Life Rev., 12, 2015, 76–77
| M. Lachowicz, M. Moszyński, Infinite Banach direct sums and diagonal C_0-semigroups with applications to a stochastic particle system, Semigroup Forum, 93, 2016, 34-70 |
M. Parisot, M. Lachowicz, A kinetic model for the formation of swarms with nonlinear interactions, Kinetic Related Models, 9, 1, 2016, 131-164 |
M. Dolfin, M. Lachowicz, Modeling opinion dynamics: How the network enhances consensus, Networks Heterogeneous Media, 10, 4, 2015, 877-896 |
M. Lachowicz, From particle systems to learning processes, Phys. Life Rev., 16, 2016, 150–151 |
M. Lachowicz, H. Leszczyński, M. Parisot, A simple kinetic equation of swarm formation: blow-up and global existence, Appl. Math. Letters, 57, 2016, 104-107 |
M. Lachowicz, M. Parisot, Z. Szymańska, Intracellular protein dynamics as a mathematical problem, Discrete Contin. Dyn. Syst. Ser. B, 21, 8, 2016, 2551-2566 |
M. Dębowski, M. El Dika, J. Malejczyk, R. Zdanowski, C. Prigent, J.-P. Tassan, M. Kloc, M. Lachowicz, J.Z. Kubiak, Flexibility vs. robustness in cell cycle control: mathematical model of interplay between CDK1, PP2A and CDC25 activities in regulation of timing of M-phase entry in Xenopus laevis embryo cell-free extract, Internat. J. Develop. Biol., 60, 2016, 305-314 |
M. Lachowicz, H. Leszczyński, M. Parisot, Blow-up and global existence for a kinetic equation of swarm formation, Math. Models Methods Appl. Sci., 27, 6, 2017, 1153-1175 |
A. Friedman, M. Lachowicz, U. Ledzewicz, M. Piotrowska, Z. Szymańska, Preface, Math. Biosciences Engin., 2017, 14, 1, 1.
| M. Lachowicz, A class of microscopic individual models corresponding to the macroscopic logistic growth, Math. Methods Appl. Sci., 41, 2018, 8446-8454 |
M. Lachowicz, A class of individual-based models, BIOMATH, 7, 1, 2018, Article ID: 1804127 |
M. Dolfin, M. Lachowicz, A. Schadschneider, A Microscopic Model of Redistribution of Individuals Inside an ‘Elevator’, Springer Nature 2018, P. Drygaś, S. Rogosin (Eds.), Modern Problems in Applied Analysis, Trends in Mathematics, 2018, 77-86 |
D. Burini, E. De Angelis, M. Lachowicz, A continuous-time Markov chain modeling cancer-immune system interactions, Commun. Appl. Indust. Math., 9 (2), 2018, 106-118 |
G. Dudziuk, M. Lachowicz, H. Leszczyński, Z. Szymańska, A simple model of collagen remodeling, Discrete Contin. Dyn. Syst. Ser. B, May 2019, 24(5): 2205-2217 |
M. Lachowicz, H. Leszczyński, K.A. Topolski, Self-organization with small range interactions: Equilibria and creation of bipolarity, Appl. Math. Computation, 343, 2019, 156-166 |
M. Dębowski, M. Lachowicz, Z. Szymańska, Microscopic description of DNA thermal denaturation, Appl. Math. Computation, 361 (2019) 47–60 |
M. Lachowicz, H. Leszczyński, E. Puźniakowska–Gałuch, Diffusive and anti-diffusive behavior for kinetic models of opinion dynamics, Symmetry, 2019, 11, 1024 |
M. Dębowski, Z. Szymańska, J.Z. Kubiak, M. Lachowicz, Mathematical Model Explaining the Role of CDC6 in the Diauxic Growth of CDK1 Activity during the M-Phase of the Cell Cycle, Cells, 8 (2019) 1537 |
M. Lachowicz, H. Leszczyński, Modeling asymmetric interactions in economy, Mathematics, 2020, 8(4), 523-537 |
M. Lachowicz, H. Leszczyński, E. Puźniakowska–Gałuch, Diffusive and anti-diffusive behavior for kinetic models of opinion dynamics, In: Kinetic Theory and Swarming Tools to Modeling Complex Systems - Symmetry problems in the Science of Living Systems, Printed Edition of the Special Issue Published in Symmetry, Ed. N. Bellomo, MPDI Basel 2020, 21-36 |
M. Lachowicz, M. Dębowski, Diauxic growth at the mesoscopic scale, Entropy, 2020, 22(11), 1280-1291 |
J. Banasiak, M. Lachowicz, Preface to the special issue BIOMATH 2019, Math. Methods Appl. Sci., 43, 18, 2020, 10359-10360.
| M. Lachowicz, H. Leszczyński, K.A. Topolski, Approximations of kinetic equations of swarm formation: Convergence and exact solutions, Appl. Math. Computation, 417, 2022, 126778, 1-16. |
M. Lachowicz, M. Matusik, K.A. Topolski, Population of entities with three individual states and asymmetric interactions, Appl. Math. Computation, 464, 1 March 2024, 128395 |
Z. Szymańska, M. Lachowicz, N. Sfakianakis, M.A.J. Chaplain, Mathematical modelling of cancer invasion: Phenotypic transitioning provides insight into multifocal foci formation, J. Computat. Science 75, 2024, 102175 |
Papers in Polish
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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. |
M. Lachowicz, Nieskończoność - nieskończenie użyteczna, Delta, 7 (470), 2013, 12. |
M. Lachowicz, Matematyka stosowana i mechanika, Delta, 4 (467), 2013, 1.. |
M. Lachowicz, Kilka uwag o matematyce stosowanej - przez matematyka stosowanego napisane, Mathematica Applicanda (Matematyka Stosowana) 42, 2014, xxxvi-xxxvii. |
M. Lachowicz, Opisy wieloskalowe - wyzwanie dla matematyki, w Metody matematyczne w zastosowaniach, tom 3, pod redakcją A. Bartłomiejczyk, Centrum Zastosowań Matematyki, Politechnika Gdańska, Gdańsk 2015, 103-119. |
M. Lachowicz, Matematyka jest strukturą świata?, Delta, 8, 2017, 3. |
M. Lachowicz, Intuicja matematyczna w Raju?, Delta, 9, 2021, 17-19. |
M. Lachowicz, Biomatematyka, instrukcja obsługi, Delta, 10, 2021, 14-16. |
M. Lachowicz, Matematyka i życie: punkty przegięcia, Delta, 11, 2021, 18-20. |
M. Lachowicz, Fibonacci prawie wszędzie, Delta, 04, 2022, 12-14. |
M. Lachowicz, Poszukiwanie jedności, czyli co ma wspólnego matematyka z leczeniem nowotworów, Szkice Nadobrzańskie, 1(4), 2022, 77-79. |
M. Lachowicz, Matematyka i literatura: J.M. Coetzee, Delta, 01, 2023, 4-5. |
M. Lachowicz, ,,Experyment'' z nieskończonością, Delta, 08, 2023, 1-3. |
M. Lachowicz, Samotność i liczby, Delta, 11, 2023, 17-19. |
M. Lachowicz, Chcę poszukiwać całości w złożoności, Pro Libris, 1, 2024, 83-88. |
Entry in Encyclopedia
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M. Lachowicz, Model matematyczny, Wielka Encyklopedia PWN, tom 17. |
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