Structural properties and finite range elementary solutions of the linear Boltzmann equation
In: Bulletin de la Classe des sciences, Band 59, Heft 1, S. 500-518
The natural solutions of the time-and energy-independent linear Boltzmann equation with isotropic scattering have been found on A ⊗ B° where A is the interval [a,b] a,b > 0 and B° = [— 1,0[⋃]0,1]. These functions are regular everywhere on A ⊗ B° and they satisfy homogeneous or inhomogeneous boundary conditions. The solutions become uniformly continuous functions on A ⊗ B and have bounded derivatives of any order if the convention for taking limits, [formule], is used. The
construction of the solutions is based on a number of structural properties established by corresponding new theorems. They exhibit invariance properties with respect to translation, partity and scaling transformations.