Non-Classical Models Of The Theory Of Boundary Value Problems.

      Аннотация: In the monograph non-classical models of the some Theory of boundary value problems are considered. Basic concepts of dynamic problems of deformable solid elastic bodies of the generalized Green-Lindsay theories of couple-stress thermo-elasticity and couple-stress thermo-diffusion for isotropic, homogeneous elastic media are study . There is worked out the general theory of solvability of dynamical problems for conjugated system of differential equations of thermo-piezoelasticity, formulated by Toupin – Mindlin, the diffusion models of linear theory of a two-component elastic mixture using the methods the Laplace integral transform, potential method and singular integral equations. effective solution of boundary value problems for a half-plane are constructed. They are solved explicitly by using the Fourier’s integrals. Approximate solution of some mixed boundary value problems for finite domain, bounded by the some closed surface are constructed. They are solved explicitly by using the generalized Fourier's series method.

Ключевые слова: The couple-stress thermo-elasticity, couple-stress thermo-diffusion, thermo-piezo-elasticity, boundary value problems.