Abstract
We investigate three-dimensional transmission problems related to
the interaction of metallic and piezoelectric ceramic bodies. We
give a mathematical formulation of the physical problem when the
metallic and ceramic sub-domains are bonded along some proper parts
of their boundaries. The corresponding nonclassical mixed boundary-transmission
problem is reduced by the potential method to an equivalent nonselfadjoint
strongly elliptic system of pseudo-differential equations on manifolds
with boundary. We investigate the solvability of this system in different
function spaces. On the basis of these results we prove uniqueness
and existence theorems for the original boundary-transmission problem.
We study also the regularity of the electrical and mechanical fields
near the curves where the boundary conditions change and where the
interfaces intersect the exterior boundary. The electrical and mechanical
fields can be decomposed into singular and more regular terms near
these curves. A power of the distance from a reference point to the
corresponding edge-curves occurs in the singular terms and describes
the regularity explicitly. We compute these complex-valued exponents
and demonstrate their dependence on the material parameters (� 2009
WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
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