Inverse Source Problem in Radiative Transport with Nonlinear Anisotropic Sources

Abstract

An inverse source problem in the stationary radiative transport in two dimension in an absorbing and scattering medium is considered, where the source is directionally quadratic polynomial. The medium has an anisotropic scattering property that is neither negligible nor large enough for the diffusion approximation to hold. The attenuating and scattering properties of the medium are assumed known. For scattering kernels of finite Fourier coefficients in the angular variable, we show how to recover the nonlinear anisotropic radiative source from boundary measurements.

Keywords:

• Nonlinear anisotropic source
• radiative transport
• source reconstruction
• scattering
• A-analytic maps

2010 Mathematics Subject Classification:

• Primary 35J56
• 30E20 Secondary 35R30
• 45E05

Disclosure statement

No potential conflict of interest was reported by the author.