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Perturbation theory, M-essential spectra of 2 x 2 operator matrices and application to transport operators

Jeribi Aref, Moalla Nedra, Yengui Sonia

Journal of Mathematics and Applications

2021

Vol. 44

35--55

In this article we give some results on perturbation theory of 2 x 2 block operator matrices on the product of Banach spaces. Furthermore, we investigate their M-essential spectra. Finally, we apply the obtained results to determine the M-essential spectra of two group transport operators with general boundary conditions in the Banach space Lp([-a, a] x [-1, 1]) x Lp([-a, a] x [-1, 1]), p ≥ 1 and a > 0.

Modelling of transient heat transport in metal films using the interval lattice Boltzmann method

Piasecka-Belkhayat A., Korczak A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2016

Vol. 64, nr 3

599--606

In the paper a description of heat transfer in one-dimensional crystalline solids is presented. The lattice Boltzmann method based on Boltzmann transport equation is used to simulate the nanoscale heat transport in thin metal films. The coupled lattice Boltzmann equations for electrons and phonons are applied to analyze the heating process of thin metal films via laser pulse. Such approach in which the parameters appearing in the problem analyzed are treated as constant values is widely used, but in the paper the interval values of relaxation times and electron-phonon coupling factor are taken into account. The problem formulated has been solved by means of the interval lattice Boltzmann method using the rules of directed interval arithmetic. In the final part of the paper the results of numerical computations are shown.

On continuous time version of two-phase cell cycle model of Tyrcha

Zwoleński P.

Mathematica Applicanda

2013

Vol. 41, No. 1

13--31

We consider a model of two-phase cell cycle in a maturity-structured cellular population, which consists of a system of first order linear partial differential equations (transport equations). The model is based on similar biological assumptions as models of Lasota-Mackey, Tyson-Hannsgen and Tyrcha. We examine behavior of the solutions of the system along characteristics, give conditions for existence of invariant density, and compare results with outcomes of generation.

W artykule rozważamy matematyczny opis dwufazowego modelu cyklu komórkowego w populacjach ze struktura dojrzałości komórkowej. Model, którym się zajmujemy, składa się z układu dwóch równań rózniczkowych cząstkowych (równań transportu) i jest budowany na podobnych biologicznych założeniach co modele Lasoty-Mackeya, Tysona-Hannsgena oraz Tyrchy. Rozwiązania otrzymanego układu równań badamy wzdłuż charakterystyk, podajemy warunki wystarczające na istnienie gęstości niezmienniczej i porównujemy wyniki z wynikami badań nad modelem Tyrchy.