On a mixed problem for the parabolic Lam'e type operator

We consider a boundary value problem for the parabolic Lam\'e type operator being a linearization of the Navier-Stokes' equations for compressible flow of Newtonian fluids. It consists of recovering a vector-function, satisfying the parabolic Lam\'e type system in a cylindrical domain, via its values and the values of the boundary stress tensor on a given part of the lateral surface of the cylinder. We prove that the problem is ill-posed in the natural spaces of smooth functions and in the corresponding H\"older spaces; besides, additional initial data do not turn the problem to a well-posed one. Using the Integral Representation's Method we obtain the Uniqueness Theorem and solvability conditions for the problem

Variability of structural and electronic properties of bulk and monolayer Si2Te3

Since the emergence of monolayer graphene as a promising two-dimensional material, many other monolayer and few-layer materials have been investigated extensively. An experimental study of few-layer Si2Te3 was recently reported, showing that the material has diverse properties for potential applications in Si-based devices ranging from fully integrated thermoelectrics to optoelectronics to chemical sensors. This material has a unique layered structure: it has a hexagonal closed-packed Te sublattice, with Si dimers occupying octahedral intercalation sites. Here we report a theoretical study of this material in both bulk and monolayer form, unveiling a fascinating array of diverse properties arising from reorientations of the silicon dimers between planes of Te atoms. The lattice constant varies up to 5% and the band gap varies up to 40% depending on dimer orientations. The monolayer band gap is 0.4 eV larger than the bulk-phase value for the lowest-energy configuration of Si dimers. These properties are, in principle, controllable by temperature and strain, making Si2T3 a promising candidate material for nanoscale mechanical, optical, and memristive devices.Comment: 9 pages, 4 figure