Solvability of the third and Fourth basic three-dimensional dynamic problems in hemitropic elasticity

The third and fourth basic dynamic problems for a three-dimensional homogeneous isotropic centrally symmetric hemitropic micropolar medium are studied. Under fairly general assumptions, the classical solvability of the problems is proved using the Fourier method.     

Three-Dimensional Boundary Value Problems of Elastothermodiffusion with Mixed Boundary Conditions

We investigate the basic boundary value problems of the connected theory of elastothermodiffusion for three-dimensional domains bounded by several closed surfaces when the same boundary conditions are fulfilled on every separate boundary surface, but these conditions differ on different groups of surfaces. Using the results of papers [1–8], we prove theorems on the existence and uniqueness of the classical solutions of these problems.     

Asymptotic distribution of the eigenvalues and eigenfunctions in basic boundary value oscillation problems in hemitropic elasticity

The basic boundary value oscillation problems for a three-dimensional elastic medium bounded by a closed surface are considered. Asymptotic formulas are derived for the eigenvalue and eigenfunction distributions in the problems.     

On the solvability of the three-dimensional first dynamic boundary value problem of hemitropic elasticity

We consider the first main dynamic boundary value problem for a three-dimensional piecewise homogeneous hemitropic micropolar medium. By using the Fourier method under sufficiently general assumptions, we prove the solvability of the problem in the classical sense.