Special Session 4: Mathematical methods in electromagnetism and related topics

Nonclassical dynamics transmission problems of generalized thermo-electro-magneto-elasticity
Otar Chkadua
Andrea Razmadze Mathematical Institute of I. Javakhishvili Tbilisi State University, Sokhumi State University
Rep of Georgia
Co-Author(s):    Otar Chkadua
Abstract:
We investigate the solvability, asymptotic analysis and regularity results of solutions to three-dimensional nonclassical dynamics problems of interaction between thermo-elastic and generalized thermo-electro-magneto-elastic homogeneous anisotropic bodies with a crack at the interface. The considered generalized thermo-electro-magneto-elasticity model is based on the Green--Lindsay theory. Unlike classical theories of thermo--elasticity, heat propagation in this model occurs with a finite speed. Using the Laplace transform, potential theory and the method of pseudodifferential equations on a manifold with a boundary based on the Wiener--Hopf factorization method, existence and uniqueness theorems are proved. Asymptotics of solutions near the edge of a interface crack and near the lines where the boundary conditions of different types meet are obtained. Based on the asymptotic analysis, we establish almost optimal H\{o}lder results for solutions. This is joint work with D. Natroshvili and T. Buchukuri. This research was supported by Shota Rustaveli National Science Foundation (SRNSF) Grant No. FR-23-267.