AN ASYMPTOTIC HOMOGENIZATION FORMULA FOR COMPLEX PERMITTIVITY AND ITS APPLICATION

Mityushev V. Gric T. Zhunussova Z. Dosmagulova K.
31 March 2023 DergiPark

Advances in the Theory of Nonlinear Analysis and its Applications
2023 #7 Issue 1 243 - 252 pp.

The R-linear boundary value problem in a multiply con-nected 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 compo-nents. A new asymptotic formula for the effective permittivity tensor is derived. The formula contains location of inclusions in symbolic form. The application of the derived formula to investigation of the morphol-ogy of the tumor cells in disordered biological media is discussed.

Asymptotic formulas , Composites , homogenization

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Faculty of Computer Science and Telecommunications, Cracow University of Technology, Kraków, Poland
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
VILNIUS TECH, Vilnius, Lithuania
Aston Institute of Photonic Technologies Aston University, Birmingham, United Kingdom
Semiconductor Physics Institute, Center for Physical Sciences and Technology, Vilnius, Lithuania
Al-Farabi Kazakh National University, Almaty, Kazakhstan
Department of Mathematics Analysis Logic and Discrete Mathematics, Ghent University, Ghent, Belgium

Faculty of Computer Science and Telecommunications
Institute of Mathematics and Mathematical Modeling
VILNIUS TECH
Aston Institute of Photonic Technologies Aston University
Semiconductor Physics Institute
Al-Farabi Kazakh National University
Department of Mathematics Analysis Logic and Discrete Mathematics

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