International Conference «Mathematical and Information Technologies, MIT-2016»

28 August – 5 September 2016

Vrnjacka Banja, Serbia – Budva, Montenegro

Susic J.  

New space of distributins with applications to photon distribution equation in the space with an infinite absorption point

We consider the equation for photon distribution as a motivation for the introduction of the new space of distributions and the corresponding weak convergence in the Colombeau algebra. We prove the existence of a solution to the corresponding Cauchy problem. We introduce a new space of distributions defined as a space of continuous linear functionals over discontinuous functions. The discontinuities are chosen so that a linear transform turns them into smooth functions implying that the new space of distributions is isomorphic to the classical Schwartz space of distributions. However, unlike the situation in the case of the Schwartz distributions, multiplication of regularization of e.g. δ-function converges toward a distribution. We use this fact to show existence of a physically reasonable solution to the photon distribution equations.
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