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Mixed boundary–transmission problems for composite layered elastic structures
Author(s) -
Natroshvili David,
Mrevlishvili Maia
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6734
Subject(s) - mathematics , sobolev space , uniqueness , mathematical analysis , boundary value problem , partial differential equation , smoothness , boundary (topology) , boundary problem , anisotropy , elasticity (physics) , type (biology) , function (biology) , physics , ecology , quantum mechanics , biology , thermodynamics , evolutionary biology
We investigate mixed type boundary–transmission problems of the generalized thermo‐electro‐magneto‐elasticity theory for complex elastic anisotropic layered structures containing interfacial cracks. This type of problems is 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.