Tengiz Buchukuri, Otar Chkadua, David Natroshvili
abstract:
The monograph is dedicated to the theoretical investigation of basic, mixed, and
crack type three-dimensional initial-boundary value problems of the generalized
thermo-electro-magneto-elasticity theory associated with Green--Lindsay's model.
The essential feature of the generalized model under consideration is that heat
propagation has a finite speed. We investigate the uniqueness of solutions to
the dynamical initial-boundary value problems and analyse the corresponding
boundary value problems of pseudo-oscillations which are obtained form the
dynamical problems by the Laplace transform. The solvability of the boundary
value problems under consideration are analyzed by the potential method in
appropriate Sobolev--Slobodetskii ($W^{s}_p$), Bessel potential ($H^{s}_p$), and
Besov ($B^{s}_{p,q}$) spaces. The smoothness properties and singularities of
thermo-mechanical and electro-magnetic fields are investigated near the crack
edges and the curves where the different types of boundary conditions collide.
Mathematics Subject Classification: 31B10, 35A15, 35A20, 35B65, 35C15, 35D30, 35J47, 35J50, 5J57, 35L51, 35L53, 35S05, 44A10, 45E05, 45E10, 45f15, 45M05, 47A50, 47G10, 47G30, 47G40, 74A15, 74A45, 74B05, 74E10, 74F05, 74F15, 74G30, 74G70, 74H20, 74H25, 74H30, 74H35
Key words and phrases: Generalized thermo-electro-magneto-elasticity, piezoelectricity, Green-Lindsay's model, initial and boundary value problems, mixed problems, crack problems, fundamental solution, transmission problems, potential method, pseudodifferential equations, asymptotic properties of solutions, stress singularity exponents