ABSTRACT
This chapter discusses far-field expansion theorem in thermoelastic scattering. Scattering theory was established as a mathematical entity by Rayleigh in a period of 50 years. A crucial instance in the development of scattering theory was the 1912 Sommerfeld’s paper, where the behavior of the scattered field at infinity was imposed by an asymptotic condition, which was dictated by the mathematical demands for well-posedness and was compatible with physical reality. Atkinson proved that the asymptotic condition of Sommerfeld can be replaced by a uniformly and absolutely convergent series representation of the scattered wave outside the smallest sphere that contains the scattering obstacle. This is an expansion in inverse powers of the radial distance and its leading term recovers Sommerfeld’s Radiation Condition. Atkinson’s theorem provides the wave analogue of Maxwell’s multipole expansion in potential theory. For Maxwell’s equations, the algorithm of reconstruction was much more complicated than the scalar case of acoustical scattering.
