The Fourier method in three-dimensional dynamical problems of the hemitropic theory of elasticity

Abstract

The basic three-dimensional dynamical problems for a hemitropic (non-centrally symmetric) micropolar elastic medium are considered. Using the Fourier method, the solvability of the formulated by us problems is proved in a classical sense. AMS Subject Classification:Key Words and Phrases: Basic Notation and EquationsLet D ⊂ R 3 be a finite domain bounded by a closed surface S of the class C 2,α ;A system of differential equations of dynamics for the hemitropic micropolar elastic medium is of the form [1, 2]:where ∆ is the three-dimensional Laplace operator; u(x, t) = (u 1 , u 2 , u 3 ) is the displacement vector; ω(x, t) = (ω 1 , ω 2 , ω 3 ) is the vector of rotation; x = (x 1 , x 2 , x 3 ) is a point in R 3 ; t is time; X(x, t) is the vector of body forces;