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The positivity principle in Boltzmann‐type equations
Author(s) -
Ebersoldt F.,
Leis R.
Publication year - 1980
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.1670020407
Subject(s) - mathematics , eigenvalues and eigenvectors , type (biology) , operator (biology) , boltzmann equation , boltzmann constant , mathematical analysis , differential equation , quantum mechanics , ecology , biochemistry , chemistry , physics , repressor , gene , transcription factor , biology
Classical theorems about matrices with non‐negative elements can be generalized for application in eigenvalue problems of integro‐differential form appearing in the description of stationary particle transport. In this way the existence and unicity of positive L 1 ‐eigensolutions of the m ‐quasi‐completely‐continuous transport operator can be deduced. These solutions can be realized by a method of successive approximation.