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Green's contact functions for heat conduction of two half‐spaces and half‐planes with application to several boundary contact problems
Author(s) -
Jentsch Lothar
Publication year - 1991
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.1670140904
Subject(s) - mathematics , boundary (topology) , mathematical analysis , bimetal , boundary value problem , thermal conduction , fredholm integral equation , plane (geometry) , integral equation , geometry , materials science , composite material
Green's contact functions are constructed for two half‐spaces and two half‐planes for materials with different thermal conductivities. With the aid of these contact functions some bimetal problems are reduced to boundary integral equations along the outer boundary where only the boundary conditions are to be satisfied. The boundary integral operators are investigated in the plane case. They are Fredholm operators with index zero. The asymptotics of the density of the potentials, which depends on the material parameters and on the angles between the contact line and the outer boundary, is determined by the Mellin transform technique.