Photon transport equations, which describe the growth of laser pulse propagating an amplifying medium, cannot be solved in closed form when a loss term is taken into account. In the previous paper, a numerical analysis was given for the equations with certain initial and boundary conditions by using the method of finite difference. However the existence of the solution and convergence of the difference scheme were not proved but assumed there.
Here we prove mathematically the unique existence of the solution in the photon transport equations when loss term is not negligible. This paper also give the outline of the proof of convergence in the upper difference scheme. The result of these proofs advances the degree of reliability of solutions calculated by the finite difference method.
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