On one-dimensional diffusion processes with moving membranes

• Autorzy: Kopytko Bohdan , Shevchuk Roman

Identyfikatory

DOI

10.17512/jamcm.2022.3.04

• Języki publikacji: EN

Abstrakty

EN

Using the method of the classical potential theory, we construct the two-parameter Feller semigroup associated, on the given interval of the real line, with the Markov proces such that it is a result of pasting together, at some point of the interval, two ordinary diffusion processes given in sub-domains of this interval. It is assumed that the position on the line of boundary points of these sub-domains depends on the time variable. In addition, some variants of the general nonlocal boundary condition of Feller-Wentzell’s type are given in these points. The resulting process can serve as a one-dimensional mathematical model of the physical phenomenon of diffusion in media with moving membranes.

Słowa kluczowe

EN

diffusion processes with membrane; two-parapeter Feller semigroup; nonlocal boundary conditions; method of potential theory

PL

procesy dyfuzyjne z membraną; półgrupa Fellera dwuparapetowa; nielokalny warunek brzegowy; metoda teorii potencjału

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2022
• Tom: Vol. 21, nr 3
• Strony: 45--57
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Kopytko Bohdan

• Department of Mathematics, Czestochowa University of Technology Czestochowa, Poland

autor

Shevchuk Roman

• Department of Mathematics, Lviv Polytechnic National University Lviv, Ukraine

Bibliografia

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• [3] Portenko, M.I. (1995). Diffusion processes in media with membranes. Institute of Mathematics of the NAS of Ukraine.
• [4] Kopytko, B.I., & Shevchuk, R.V. (2013). Diffusions in one-dimensional bounded domains with reflection, absorption and jumps at the boundary and at some interior point. J. Appl. Math. Comput. Mech., 12(1), 55-68.
• [5] Kopytko, B.I., & Shevchuk, R.V. (2020). One-dimensional diffusion processes with moving membrane: partial reflection in combination with jump-like exit of process from membrane. Electron. J. Probab., 25, 1-21.
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• [8] Pilipenko, A.Yu. (2012). On the Skorokhod mapping for equations with reflection and possible jump-like exit from a boundary. Ukrainian Math. J., 63(9), 1415-1432.
• [9] Taira, K. (2014). Semigroups, Boundary Value Problems and Markov Processes. Springer Monographs in Mathematics.
• [10] Arendt, W., Kunkel, S., & Kunze, M. (2016). Diffusion with nonlocal boundary conditions. J. Funct. Anal., 270(7), 2483-2507.
• [11] Ladyzhenskaya, O.A., Solonnikov, V.A., & Ural’tseva, N.N. (1967). Linear and quasilinear equations of parabolic type. Nauka.
• [12] Friedman, A. (2013). Partial differential equations of parabolic type. Dover Publications.
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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).