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\begin{document}

\title{Mixed boundary-transmission problems for composite layered elastic
structures}



\author[1]{David Natroshvili}%
\author[1]{Maia Mrevlishvili}%
\affil[1]{Georgian Technical University}%


\vspace{-1em}



  
  \date{May 10, 2024}


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\begin{abstract}
We investigate mixed type boundary-transmission problems of the
generalized thermo-electro-magneto elasticity (GTEME) theory for complex
elastic anisotropic layered structures containing interfacial cracks.
This type of problems are described mathematically by systems of partial
differential equations with appropriate transmission and boundary
conditions for six dimensional unknown physical field (three components
of the displacement vector, electric potential function, magnetic
potential function, and temperature distribution function). We apply the
potential method and the theory of pseudodifferential equations and
prove uniqueness and existence theorems of solutions to different type
mixed boundary-transmission problems in appropriate Sobolev spaces. We
analyze smoothness properties of solutions near the edges of interfacial
cracks and near the curves where different type boundary conditions
collide.%
\end{abstract}%



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