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On existence of solutions for a system of Boltzmann transport equations
Author(s) -
Tervo Jouko
Publication year - 2008
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1072
Subject(s) - boltzmann equation , uniqueness , operator (biology) , mathematics , boundary value problem , particle system , boltzmann constant , inflow , boundary (topology) , convection–diffusion equation , particle (ecology) , mathematical analysis , physics , mechanics , computer science , chemistry , thermodynamics , oceanography , repressor , gene , transcription factor , geology , operating system , biochemistry
We consider a linear system of Boltzmann transport equations. The system models charged particle transport in tissue, for example. Although only one species of particles, say photons, is invasing these particles mobilize electrons and positrons. Hence in realistic modelling of particle transport one needs a coupled system of three Boltzmann transport equations. The solution of this system must satisfy the inflow boundary condition. We show existence and uniqueness result of the solution applying coercitivity of the underlying linear operator and its adjoint operator. In addition, we consider existence of continuous solutions by iterative methods. Copyright © 2008 John Wiley & Sons, Ltd.