- ISSN: 2587-2648
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Vladimir Mityushev, Tatjana Gric, Zhanat Zhunussova, Karlygash Dosmagulova
Vladimir Mityushev
Faculty of Computer Science and Telecommunications, Cracow University of Technology, Kraków, Poland
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Tatjana Gric
VILNIUS TECH, Vilnius, Lithuania
Aston Institute of Photonic Technologies, Aston University, Birmingham, UK
Semiconductor Physics Institute, Center for Physical Sciences and Technology, Vilnius, Lithuania
Zhanat Zhunussova
Al-Farabi Kazakh National University, Almaty, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Karlygash Dosmagulova
Al-Farabi Kazakh National University, Almaty, Kazakhstan
Department of Mathematics: Analysis, Logic, and Discrete Mathematics, Ghent University, Ghent, Belgium
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
The ℝ-linear boundary value problem in a multiply connected domain on a flat torus is considered. This problem is closely related to the Riemann–Hilbert problem on analytic functions. The considered problem arises in the homogenization procedure of random media with complex constants which express the permittivity of components. A new asymptotic formula for the effective permittivity tensor is derived. The formula contains the location of inclusions in symbolic form. The application of the derived formula to the investigation of the morphology of tumor cells in disordered biological media is discussed.
Keywords: Composites, Asymptotic formulas, homogenization
Mityushev, V., Gric, T., Zhunussova, Z. K., & Dosmagulova, K. (2023). An asymptotic homogenization formula for complex permittivity and its application. Advances in the Theory of Nonlinear Analysis and its Application, 7(1), 243-252.