Study of the boundary conditions describing the contact with a well-stirred fluid

The authors study the asymptotic behavior of a 1-D diffraction problem when the conductivity of one of the two media in contact becomes infinite. It is established, by means of heat potentials and Laplace transforms, that the temperature of the good conductor (well-stirred fluid) is spatially constant and the contact conditions between the two media, involving time derivatives, are found. The convergence of the solution of the diffraction problem to the solution of the well-stirred problem in the L1 norm is proved and an upper bound for the difference between these two solutions is established