Janusz Mierczynski - English version

Janusz Mierczyński

[Strona w języku polskim (informacje dla studentów)]

Useful links

arXiv.org

Permanent address	LaTeX encoding

Janusz Mierczyński		Janusz Mierczy\'nski
Department of Pure Mathematics		Department of Pure Mathematics
Faculty of Pure and Applied Mathematics		Faculty of Pure and Applied Mathematics
Wrocław University of Science and Technology		Wroc{\l}aw University of Science and Technology
Wybrzeże Wyspiańskiego 27		Wybrze\.ze Wyspia\'nskiego 27
PL-50-370 Wrocław		PL-50-370 Wroc{\l}aw
Poland		Poland
phone: +48 713202108
fax: +48 713280751
e-mail: mierczyn at pwr.edu.pl
URL: http://prac.im.pwr.edu.pl/~mierczyn/

Pronunciation (IPA 2015)

name: ˈjanuʂ mʲjɛrˈ ͡ʈʂɨɲ̟skʲi
city: ˈvrɔt͡swaf

Identifiers

Orcid: 0000-0002-1663-0723
Web of Science ResearcherID: J-8221-2012
Publons: a/1324829
MathSciNet (Mathematical Reviews): 124430
Mathematics Genealogy Project: 175589

Degrees

M. Sc. in Mathematics, University of Wrocław, 1980
Ph. D. in Mathematics, Wrocław University of Technology, 1983
Habilitation in Mathematics, Wrocław University of Technology, 1998
Professor’s title, conferred by the President of the Republic of Poland in 2013

Research interests

Strongly monotone dynamical systems
Principal spectrum of random and nonautonomous parabolic partial differential equations of second order
Persistence in competitive systems of ordinary and partial differential equations of Kolmogorov type

Google Scholar

Publons

Internationally funded research projects

o U.S.-Polish Cooperative Research: Lyapunov Exponents and Spectrum for Random and Nonautonomous Parabolic Equations (2004 – 2007) – Principal Investigator

Community service

IOP Publishing Trusted Reviewer Certificate

Conferences

Past:

o Celebrating the mathematics of Michel Benaïm, The Bernoulli Center for Fundamental Studies, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland, August 21 – 24, 2023. (link to some pictures) (link to the slides, with some misprints corrected)

o Nonautonomous Dynamics and Applications, workshop, Department of Applied Mathematics, Universidad de Valladolid, Valladolid, Spain, November 25 – 27, 2015.

o VII Symposium on Nonlinear Analysis, Toruń, Poland, September 14 – 18, 2015.

The 10^th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Madrid, Spain, July 7 – July 11, 2014.
Dynamics Day, The Finnish Centre of Excellence in Analysis and Dynamics Research, University of Helsinki, Helsinki, Finland, October 9, 2013.
Dynamical Methods for Differential Equations with Applications, workshop, Department of Applied Mathematics, Universidad de Valladolid, Valladolid, Spain, September 10 – 11, 2012.
8^th European Conference on Mathematical and Theoretical Biology, Kraków, Poland, June 28 – July 2, 2011.
Dynamical Systems Meeting – Lower Silesia 2010, Trzebieszowice, Poland, May 23 – 29, 2010.
Mathematical Tools for Multi-Scale Biological Processes, Montana State University, Bozeman, MT, U.S.A., June 4 – 6, 2008.
Mini-Workshop on Differential Equations and Applications, Auburn University, Auburn, AL, U.S.A., May 28, 2008.
Rocky Mountain Conference on Dynamical Systems – Stochastic Dynamics, Park City, UT, U.S.A., May 15 – 16, 2008.
International Conference on Dynamical Methods and Mathematical Modelling in honor of Russell Johnson, Valladolid, Spain, September 18– 22, 2007.
Workshop on Ergodic Theory and Dynamical Systems, Szklarska Poręba, Poland, June 18 – 24, 2006.
International Conference on Non-autonomous & Stochastic Dynamical Systems, Sevilla, Spain, September 27 – October 1, 2005.
First International Conference on Recent Advances in Bifurcation Theory and Applications of Dynamical Systems, Jinhua, China, June 8 – 12, 2005.
International Conference on Nonlinear Dynamics and Evolution Equations, St. John’s, NL, Canada, July 6 – 10, 2004.
SIAM Conference on Applications of Dynamical Systems, Snowbird, UT, U.S.A., May 27 – 31, 2003.

Links to mathematicians I have had the hono(u)r to collaborate with

Ph. D. students

Past:

Joanna Balbus (née Pętela), Ph. D. conferred in December 2011

Present:

Marek Kryspin

(joint with Wenxian Shen) Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications, Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics, 139, Chapman & Hall/CRC, Boca Raton, FL, 328 pages, ISBN: 9781584888956, ISBN-10: 1584888954, published March 24, 2008.

Abstract:

The goal of the monograph is to give a clear and essentially self-contained account of the spectral theory, in particular, the theory of principal spectrum and principal Lyapunov exponents for general time dependent and random linear parabolic equations of second order on bounded domain, as well as systems of such equations. Also, applications to uniform persistence in nonlinear Kolmogorov systems are given.

The monograph gives a unified approach to the theory of principal spectrum: It starts from the abstract general theory, in the framework of weak solutions, and then specializes to the cases of random and nonautonomous equations. Fundamental properties of the principal spectrum/principal Lyapunov exponents are investigated. The book contains many new results, as well as it puts already known results in a new perspective.

The intended readership of the monograph are research mathematicians and Ph. D. students in mathematics, in particular (but not limited to) those specializing in applications of mathematics to ecology.

Table of contents:

Introduction
Fundamental Properties in the General Setting
Spectral Theory in the General Setting
Spectral Theory in Nonautonomous and Random Cases
Influence of Spatial-Temporal Variations and the Shape of Domain
Cooperative Systems of Parabolic Equations
Applications to Kolmogorov Systems of Parabolic Equations

Ordering:

CRCnetBase book page

Reviews:

“The monograph gives a clear and interesting account of the principal spectral theory for general time-dependent and random linear parabolic equations and systems. It contains many new results and puts some already known results in a new framework. …”

Krystyna Twardowska, Mathematical Reviews, Issue 2010g (link to the review)

Sample papers

[List of all publications]

(if your institution is not a subscriber to the MR or a journal, e-mail me: mierczyn at pwr.edu.pl)

Preprints:

o (joint with Marek Kryspin) Systems of parabolic equations with delays: Continuous dependence on parameters. (link to the preprint at arXiv)

o (joint with Marek Kryspin, Sylvia Novo and Rafael Obaya) Two dynamical approaches to the notion of exponential separation for random systems of delay differential equations. (link to the preprint at arXiv)

Non-refereed notes:

o Flows on ordered bundles, 1995. (.pdf version)

Refereed papers:

o (joint with Stephen Baigent) Existence of the carrying simplex for a retrotone map, J. Difference Equ. Appl. 30(3) (2023), pp. 287–319. (link to the journal) (for an earlier version, Existence of the carrying simplex for a C¹ retrotone map, see arXiv)

o (joint with Marek Kryspin) Parabolic differential equations with bounded delay, J. Evol. Equ. 23:2 (2023). (link to the preprint at arXiv) (link to the journal)

o The C¹ property of convex carrying simplices for competitive maps, Ergodic Theory Dynam. Systems, 40(5) (2020), pp. 1335-1350. (accepted version) (final version, requires access to CUP) (final version, read-only)

o (joint with Sylvia Novo and Rafael Obaya) Lyapunov exponents and Oseledets decomposition in random dynamical systems generated by systems of delay differential equations, Commun. Pure Appl. Anal. 19(4), April 2020, special issue in honour of Prof. Tomás Caraballo on occasion of his 60th birthday, pp. 2235-2255. (link to the journal) (link to the preprint at arXiv)

o (joint with Lei Niu and Alfonso Ruiz-Herrera) Linearization and invariant manifolds on the carrying simplex for competitive maps, J. Differential Equations, 267(12) (2019), pp. 7385-7410. (accepted version) (link to the journal, may require institutional access or payment)

o (joint with Sylvia Novo and Rafael Obaya) Principal Floquet subspaces and exponential separations of type II with applications to random delay differential equations, Discrete Contin. Dyn. Syst. 38(12), December 2018, Special issue on Llavefest (in honor of Rafael de la Llave), pp. 6163-6193. (link to the journal) (link to the preprint at arXiv) MR3917806 (link to the review)

o The C¹ property of convex carrying simplices for three-dimensional competitive maps, J. Difference Equ. Appl. 24(8) (2018), pp. 1199-1209. (accepted version) (link to the journal) (link to the preprint at arXiv)

o Instability in linear cooperative systems of ordinary differential equations, SIAM Rev. 59(3) (2017), pp. 649-670. (publisher’s version, without supplements or interactive material) (link to the journal) MR 3683685 (link to the review)

o (joint with Wenxian Shen) Formulas for generalized principal Lyapunov exponent for parabolic PDEs, Discrete Contin. Dyn. Syst. Ser. S 9 (4) (2016), pp. 1189-1199. (link to the journal) (link to the preprint at arXiv) MR 3543652

o (joint with Wenxian Shen) Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. III. Parabolic equations and delay systems, J. Dynam. Differential Equations 28(3-4) (2016), pp. 1039-1079. (link to the journal) (publisher's version) MR 3537364 (link to the review)

o Averaging in random systems of nonnegative matrices, Discrete Contin. Dyn. Syst. (2015), Dynamical systems, differential equations and applications, 10th AIMS Conference, Suppl., pp. 835-840. (link to the journal) (link to the preprint at arXiv) MR 3462519

o Lower estimates of top Lyapunov exponent for cooperative random systems of linear ODEs, Proc. Amer. Math. Soc. 143(3) (2015), pp. 1127-1135. (link to the journal) (link to the preprint at arXiv) MR 3293728 (link to the review)

o Estimates for principal Lyapunov exponents: A survey, Nonauton. Dyn. Syst. 1 (2014), pp. 137-162. (link to the journal) (link to the preprint at arXiv) MR 3378314 (link to the review)

o (joint with Wenxian Shen) Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. II. Finite-dimensional systems, J. Math. Anal. Appl. 404(2) (2013), pp. 438-458. (link to the journal) (link to the preprint at arXiv) MR 3045185

(joint with Wenxian Shen) Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. I. General theory, Trans. Amer. Math. Soc. 365(10) (2013), pp. 5329-5365. (link to the journal) (link to the preprint at arXiv) MR 3074376 (link to the review)
(joint with Murad Banaji) Global convergence in systems of differential equations arising from chemical reaction networks, J. Differential Equations 254(3) (2013), pp. 1359-1374 (link to the journal) (link to the preprint at arXiv) MR 2997375
(joint with Joanna Balbus) Time-averaging and permanence in nonautonomous competitive systems of PDEs via Vance-Coddington estimates, Discrete Contin. Dyn. Syst. Ser. B 17(5) (2012), pp. 1407-1425. (link to the journal) MR 2903759
(joint with Wenxian Shen) Persistence in forward nonautonomous competitive systems of parabolic equations, J. Dynam. Differential Equations 23(3) (2011), pp. 551-571. (link to the journal) MR 2836650 (2012j:35172)
(joint with Wenxian Shen) Spectral theory for forward nonautonomous parabolic equations and applications, Fields Inst. Commun., 64, pp. 57-99, (Proceedings of the International Conference on Infinite Dimensional Dynamical Systems, York University, Toronto, September 24 – 28, 2008, dedicated to Professor George Sell on the occasion of his 70th birthday), Springer, New York, 2013. (link to the book chapter) MR 2986931
(joint with Jifa Jiang and Yi Wang) Smoothness of the carrying simplex for discrete-time competitive dynamical systems: A characterization of neat embedding, J. Differential Equations 246(4) (2009), pp. 1623-1672 (link to the journal). MR 2488699 (2010b:37066) (link to the review)
(joint with Wenxian Shen) Time averaging for nonautonomous/random linear parabolic equations, Discrete Contin. Dyn. Syst. Ser. B 9(3/4) (2008), pp. 661-699 (link to the journal). MR 2379432 (2009a:35108) (link to the review)
(joint with Wenxian Shen) The Faber–Krahn inequality for random/nonautonomous parabolic equations, Commun. Pure Appl. Anal. 4(1) (2005), pp. 101-114 (link to the journal). MR 2126280 (2006b:35358) (link to the review)
(joint with Wenxian Shen and Xiaoqiang Zhao) Uniform persistence for nonautonomous and random parabolic Kolmogorov systems, J. Differential Equations 204(2) (2004), pp. 471-510 (link to the journal). MR 2085544 (2006f:37111) (link to the review)
(joint with Wenxian Shen) Lyapunov exponents and asymptotic dynamics in random Kolmogorov models, J. Evol. Equ. 4(3) (2004), pp. 371-390 (link to the journal). MR 2120129 (2005k:37122) (link to the review)
(joint with Wenxian Shen) Exponential separation and principal Lyapunov exponent/spectrum for random/nonautonomous parabolic equations, J. Differential Equations 191(1) (2003), pp. 175-205 (link to the journal). MR 1973287 (2004h:35232) (link to the review)
(joint with Sebastian J. Schreiber) Kolmogorov vector fields with robustly permanent subsystems, J. Math. Anal. Appl. 267(1) (2002), pp. 329-337 (link to the journal). MR 1886831 (2003b:37041) (link to the review)
The principal spectrum for linear nonautonomous parabolic PDEs of second order: Basic properties, J. Differential Equations 168(2) (2000), pp. 453-476 (link to the journal). MR 1808456 (2001m:35147) (link to the review)
On peaks in carrying simplices, Colloq. Math. 81(2) (1999), pp. 285-292 (link to the journal). MR 1715352 (2000j:37029) (link to the review)
Smoothness of unordered curves in two-dimensional strongly competitive systems, Appl. Math. (Warsaw) 25(4) (1999), pp. 449-455 (link to the journal). MR 1687364 (2000f:34089) (link to the review)
Smoothness of carrying simplices for three-dimensional competitive systems: A counterexample, Dynam. Contin. Discrete Impuls. Systems 6(1) (1999), pp. 149-154 (see the paper in dvi, ps, pdf form). MR 1679762 (2000a:34095) (link to the review)
On smoothness of carrying simplices, Proc. Amer. Math. Soc. 127(2) (1999), pp. 543-551 (link to the journal). MR 1606000 (99c:34086) (link to the review)
Globally positive solutions of linear parabolic partial differential equations of second order with Dirichlet boundary conditions, J. Math. Anal. Appl. 226(2) (1998), pp. 326-347 (link to the journal). MR 1650236 (99m:35096) (link to the review)
Three-dimensional cooperative irreducible systems with a first integral, Colloq. Math. 76(2) (1998), pp. 181-190 (link to the journal). MR 1618684 (99a:34104) (link to the review)
Invariant manifolds for one-dimensional parabolic partial differential equations of second order, Colloq. Math. 75(2) (1998), pp. 285-314 (link to the journal). MR 1490694 (98m:35090) (link to the review)
Uniqueness for quasimonotone systems with strongly monotone first integral, in: Proceedings of the Second World Congress of Nonlinear Analysts, Vol. 3 (Athens, 1996), Nonlinear Anal. 30(3) (1997), pp. 1905-1909 (link to the journal). MR 1490100 (98j:34005) (link to the review)
Globally positive solutions of linear parabolic PDE's of second order with Robin boundary conditions, J. Math. Anal. Appl. 209(1) (1997), pp. 47-59 (link to the journal). MR 1444510 (98c:35071) (link to the review).
Cooperative irreducible systems of ordinary differential equations with first integral, status unknown (was to appear in: Proceedings of the Second Marrakesh Conference of Differential Equations (1995)) (link to the paper at arXiv).
Uniqueness for a class of cooperative systems of ordinary differential equations, Colloq. Math. 67(1) (1994), pp. 21-23 (link to the journal). MR 1292940 (95j:34006) (link to the review)
The C¹ property of carrying simplices for a class of competitive systems of ODEs, J. Differential Equations 111(2) (1994), pp. 385-409 (link to the journal). MR 1284419 (95g:34066) (link to the review)
P-arcs in strongly monotone discrete-time dynamical systems, Differential Integral Equations 7(5-6) (1994), pp. 1473-1494 (link to the paper). MR 1269666 (95c:58121) (link to the review)
On monotone trajectories, Proc. Amer. Math. Soc. 113(2) (1991), pp. 537-544 (link to the journal). MR 1056682 (91m:54053) (link to the review)
A class of strongly cooperative systems without compactness, Colloq. Math. 62(1) (1991), pp. 43-47 (link to the journal). MR 1114618 (92g:34056) (link to the review)
(joint with Peter Poláčik) Group actions on strongly monotone dynamical systems, Math. Ann. 283 (1989), pp. 1-11 (link to the journal). MR 0973801 (90k:58182) (link to the review)
Strictly cooperative systems with a first integral, SIAM J. Math. Anal. 18(3) (1987), pp. 642-646 (publisher’s version). MR 0883558 (88e:34093) (link to the review)

[List of all papers]

Citations

o Google Scholar

Trivia

My Erdős number is bounded above by four:

Pál Erdős – Vilmos Komornik – Alain Haraux – Peter Poláčik – J. M.,

Pál Erdős – Richard R. Hall – Hal L. Smith – Xiaoqiang Zhao – J. M.,

or else

Pál Erdős – LeRoy B. Beasley – Chi-Kwong Li – Sebastian J. Schreiber – J. M.

According to the Mathematics Genealogy Project, I have among my academic ancestors:

o mathematicians: Jean Le Rond d’Alembert, Johann Bernoulli, Jakob Bernoulli, Michel Chasles, Pafnutii Chebyshev, Gaston Darboux, Gustav Peter Lejeune Dirichlet, Leonhard Euler, Jean-Baptiste Joseph Fourier, Carl Friedrich Gauss, Felix Klein, Ernst Kummer, Joseph Louis Lagrange, Pierre Simon de Laplace, Gottfried Wilhelm Leibniz, Ferdinand Lindemann, Rudolph Lipschitz, Nikolai Lobachevskii, Andrei Markov, Stefan Mazurkiewicz, Marin Mersenne, Johann Friedrich Pfaff, Émile Picard, Julius Plücker, Simeon Denis Poisson, Wacław Sierpiński, Stanisław Zaremba

o physicists: Giovanni Battista Beccaria (not the lawyer Cesare Beccaria!), Hermann von Helmholtz, Heinrich Hertz, Christiaan Huygens, Wojciech Rubinowicz, Arnold Sommerfeld

o astronomers: Tycho Brahe, Johannes Kepler, Mikołaj Kopernik (Nicolaus Copernicus), Johannes Müller von Königsberg (Regiomontanus), Jemme Reinerszoon (Gemma Frisius), Georg Joachim Rheticus, Willebrord Snel van Royen (Snellius), Nasir al-Din al-Tusi

o physicians/anatomists: Franz de la Boë (Franciscus Sylvius), Herman Boerhaave, Jacques Dubois (Jacobus Sylvius), Girolamo Fabrizio (Hieronymus Fabricius), Gabriele Falloppio, Andreas Vesalius

o philosophers: Marsilio Ficino, Georgios Gemistos (Plethon), Nicolas Malebranche, Angelo Poliziano, Pietro Pomponazzi

o classical scholar: Johann Reuchlin

o scholars of wide interests: Basilios Bessarion, Guillaume Budé, Desiderius Erasmus of Rotterdam, Ján Jesenský (Jan Jesenius), Nicole Oresme

o “educators”: Pierre de La Ramée (Petrus Ramus), Philipp Schwarzerdt (Philipp Melanchthon), Johannes Sturm

o lawyer: Jean Calvin (the same person, but not as a theologian!)

o theologians:

o Catholic: Geert Groote, Thomas à Kempis

o Orthodox: Saint Gregory Palamas

o Protestant: Thomas Cranmer, Jakob Hermanszoon (Jacobus Arminius)

Last modified March 24, 2024

Permanent address

LaTeX encoding