| dr hab. Kazimierz Piechór |
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Habilitacja
| 1992 | Dyskretne modele równania Boltzmanna. Struktura operatora zderzeniowego. Propagacja dźwięku |
Promotor prac doktorskich
| 1. | 2007-10-25 | Kruglenko Eleonora | Analiza funkcjonałów niewypukłych charakteryzujących mikromagnetyki | 606 |
Ostatnie publikacje
| 1. | Piechór K., Calcium Waves in Thin Visco-Elastic Cells, MATHEMATICAL MODELLING OF NATURAL PHENOMENA, ISSN: 0973-5348, DOI: 10.1051/mmnp/20138313, Vol.8, No.3, pp.206-226, 2013 Streszczenie: The model we consider treats the cell as a viscoelastic medium lling one of two kinds of thin domains (\shapes" of cells): the thin slab being a caricature of a tissue and the thin circular cylinder mimicking a long cell. This enables us to simplify the system of mechano-chemical equations. We construct abundant classes of explicit, but approximate, formulae for heteroclinic solutions to these equations. Słowa kluczowe: calcium waves, mechano-chemical coupling, thin domains Afiliacje autorów:
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| 2. | Piechór K., Reaction-diffusion equation modelling calcium waves with fast buffering in visco-elastic environment, ARCHIVES OF MECHANICS, ISSN: 0373-2029, Vol.64, No.5, pp.477-509, 2012 | | 20p. | |||||||||||
| 3. | Kaźmierczak B., Piechór K., Traveling wave solutions of a model of skin pattern formation in a singular case, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, ISSN: 0170-4214, DOI: 10.1002/mma.1359, Vol.34, No.3, pp.325-337, 2011 Streszczenie: We study traveling wave solutions to a system of four non-linear partial differential equations, which arise in a tissue interaction model for skin morphogenesis. Under the assumption that the strength of attachment of the epidermis to the basal lamina is sufficiently large, we prove the existence and uniqueness (up to a translation) of traveling wave solutions connecting two stationary states of the system with the dermis and epidermis cell densities being positive. We discuss the problem of the minimal wave speed. Słowa kluczowe: skin morphogenesis, heteroclinic solutions, implicit function theorem Afiliacje autorów:
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| 4. | Piechór K., Forms of travelling waves admitted by a mechanochemical model of tumour angiogenesis, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, ISSN: 0170-4214, Vol.33, pp.1482-1495, 2010 | | 20p. | |||||||||||
| 5. | Piechór K., Non-local Korteweg stresses from kinetic theory point of view, ARCHIVES OF MECHANICS, ISSN: 0373-2029, Vol.60, No.1, pp.23-58, 2008 | | ||||||||||||
| 6. | Bobrowski A.♦, Lipniacki T., Piechór K., Rudnicki R.♦, Asymptotic behavior of distributions of mRNA and protein levels in a model of stochastic gene expression, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, ISSN: 0022-247X, DOI: 10.1016/j.jmaa.2006.11.043, Vol.333, No.2, pp.753-769, 2007 Streszczenie: The paper is devoted to a stochastic process introduced in the recent paper by Lipniacki et al. [T. Lipniacki, P. Paszek, A. Marciniak-Czochra, A.R. Brasier, M. Kimmel, Transcriptional stochasticity in gene expression, J. Theor. Biol. 238 (2006) 348–367] in modelling gene expression in eukaryotes. Starting from the full generator of the process we show that its distributions satisfy a (Fokker–Planck-type) system of partial differential equations. Then, we construct a c0 Markov semigroup in L1 space corresponding to this system. The main result of the paper is asymptotic stability of the involved semigroup in the set of densities. Słowa kluczowe: Piece-wise deterministic process, Stochastic gene expression, Semigroups of operators, Feller semigroups, Dual semigroups, Markov semigroups, Asymptotic stability Afiliacje autorów:
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| 7. | Piechór K., Dyskretne modele równania Boltzmanna: struktura operatora zderzeniowego. Propagacja dźwięku (Praca habilitacyjna), Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.2, pp.1-65, 1992 | |||||||||||||
| 8. | Fiszdon W., Piechór K., Pewne ścisłe rozwiązania równania Boltzmanna i wpływ zaburzenia potencjału oddziaływań, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.35, pp.1-46, 1970 |