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Radially symmetric solutions of the Poisson–Boltzmann equation
Author(s) -
Krzywicki A.,
Nadzieja T.,
Meister E.
Publication year - 1989
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.1670110307
Subject(s) - poisson–boltzmann equation , cylinder , mathematics , boltzmann equation , poisson's equation , mathematical analysis , container (type theory) , boundary value problem , poisson distribution , boundary (topology) , geometry , physics , thermodynamics , quantum mechanics , materials science , ion , composite material , statistics
Abstract The electrostatic potential u outside of a charged cylinder contained in an infinitely large container of electrolyte satisfies the Poisson–Boltzmann equation Δ u = shu and boundary condition ∂ u /∂ n = − σ on the cylinder and u (∞) = 0. We show that there exists a unique radially symmetric solution of the problem and consider its properties.