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Integral formulation for a steady‐state transport process with general boundary conditions
Author(s) -
Busoni G.,
Frosali G.,
Neunzert H.
Publication year - 1984
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.1670060106
Subject(s) - mathematics , eigenvalues and eigenvectors , operator (biology) , boundary value problem , mathematical analysis , boundary (topology) , integral equation , poincaré–steklov operator , steady state (chemistry) , homogeneous , robin boundary condition , mixed boundary condition , physics , biochemistry , chemistry , repressor , quantum mechanics , combinatorics , transcription factor , gene
A linear equation for a particle steady‐state transport process in a homogeneous slab of finite thickness with boundary conditions of general type is derived. This equation differs from the well‐known integral equation for no‐reentry boundary conditions because of the presence of a per‐turbance linear operator which describes the effect of the re‐emission of the particles incident at the wall. The properties of the resulting operator are investigated. The dependence of the first positive eigenvalue on physical parameters is studies in detail. The results obtained are enough to discuss the existence of a critical strictly positive solution of the physical problems which motivated this research.