Poisson-Boltzmann equation in ℝ³

A. Krzywicki; T. Nadzieja

Annales Polonici Mathematici (1991)

  • Volume: 54, Issue: 2, page 125-134
  • ISSN: 0066-2216

Abstract

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The electric potential u in a solute of electrolyte satisfies the equation Δu(x) = f(u(x)), x ∈ Ω ⊂ ℝ³, u | ∂ Ω = 0 . One studies the existence of a solution of the problem and its properties.

How to cite

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A. Krzywicki, and T. Nadzieja. "Poisson-Boltzmann equation in ℝ³." Annales Polonici Mathematici 54.2 (1991): 125-134. <http://eudml.org/doc/262418>.

@article{A1991,
abstract = {The electric potential u in a solute of electrolyte satisfies the equation Δu(x) = f(u(x)), x ∈ Ω ⊂ ℝ³, $u|_\{∂Ω\} = 0$. One studies the existence of a solution of the problem and its properties.},
author = {A. Krzywicki, T. Nadzieja},
journal = {Annales Polonici Mathematici},
keywords = {Poisson-Boltzmann equation; existence of solution; uniqueness; convergence; Dirichlet problems; existence},
language = {eng},
number = {2},
pages = {125-134},
title = {Poisson-Boltzmann equation in ℝ³},
url = {http://eudml.org/doc/262418},
volume = {54},
year = {1991},
}

TY - JOUR
AU - A. Krzywicki
AU - T. Nadzieja
TI - Poisson-Boltzmann equation in ℝ³
JO - Annales Polonici Mathematici
PY - 1991
VL - 54
IS - 2
SP - 125
EP - 134
AB - The electric potential u in a solute of electrolyte satisfies the equation Δu(x) = f(u(x)), x ∈ Ω ⊂ ℝ³, $u|_{∂Ω} = 0$. One studies the existence of a solution of the problem and its properties.
LA - eng
KW - Poisson-Boltzmann equation; existence of solution; uniqueness; convergence; Dirichlet problems; existence
UR - http://eudml.org/doc/262418
ER -

References

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  1. [1] R. Courant, Partial Differential Equations, Interscience, New York London 1962. Zbl0099.29504
  2. [2] A. Friedman and K. Tintarev, Boundary asymptotics for solutions of the Poisson-Boltzmann equation, J. Differential Equations 69 (1987), 15-38. Zbl0637.35035
  3. [3] A. Krzywicki and T. Nadzieja, Radially symmetric Poisson-Boltzmann equation in a domain expanding to infinity, submitted. Zbl0722.34016
  4. [4] W. Pogorzelski, Integral Equations and their Applications, Pergamon Press and PWN, 1969. 
  5. [5] I. Rubinstein, Counterion condensation as an exact limiting property of solution of the Poisson-Boltzmann equation, SIAM J. Appl. Math. 46 (1986), 1024-1038. Zbl0632.76106

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