Radially symmetric solutions of the Poisson-Boltzmann equation with a given energy

Tadeusz Nadzieja; Andrzej Raczyński

Applicationes Mathematicae (2000)

  • Volume: 27, Issue: 4, page 465-473
  • ISSN: 1233-7234

Abstract

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We consider the following problem: Δ Φ = ± M ο v e r ∫ Ω e - Φ / Θ e - Φ / Θ , E = M Θ ∓ 1 ο v e r 2 ∫ Ω | ∇ Φ | 2 , Φ | ∂ Ω = 0 , where Φ: Ω ⊂ ℝ n → ℝ is an unknown function, Θ is an unknown constant and M, E are given parameters.

How to cite

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Nadzieja, Tadeusz, and Raczyński, Andrzej. "Radially symmetric solutions of the Poisson-Boltzmann equation with a given energy." Applicationes Mathematicae 27.4 (2000): 465-473. <http://eudml.org/doc/219289>.

@article{Nadzieja2000,
abstract = {We consider the following problem: $ΔΦ = ± \{M οver \int _\{Ω\} e^\{- Φ/Θ\}\} e^\{- Φ/Θ\}, E = MΘ ∓ \{1οver2\}\int _\{Ω\} |∇Φ|^2, Φ|_\{\partial Ω\} = 0,$ where Φ: Ω ⊂ $ℝ^n$ → ℝ is an unknown function, Θ is an unknown constant and M, E are given parameters.},
author = {Nadzieja, Tadeusz, Raczyński, Andrzej},
journal = {Applicationes Mathematicae},
keywords = {nonlinear elliptic problem; Poisson-Boltzmann equation},
language = {eng},
number = {4},
pages = {465-473},
title = {Radially symmetric solutions of the Poisson-Boltzmann equation with a given energy},
url = {http://eudml.org/doc/219289},
volume = {27},
year = {2000},
}

TY - JOUR
AU - Nadzieja, Tadeusz
AU - Raczyński, Andrzej
TI - Radially symmetric solutions of the Poisson-Boltzmann equation with a given energy
JO - Applicationes Mathematicae
PY - 2000
VL - 27
IS - 4
SP - 465
EP - 473
AB - We consider the following problem: $ΔΦ = ± {M οver \int _{Ω} e^{- Φ/Θ}} e^{- Φ/Θ}, E = MΘ ∓ {1οver2}\int _{Ω} |∇Φ|^2, Φ|_{\partial Ω} = 0,$ where Φ: Ω ⊂ $ℝ^n$ → ℝ is an unknown function, Θ is an unknown constant and M, E are given parameters.
LA - eng
KW - nonlinear elliptic problem; Poisson-Boltzmann equation
UR - http://eudml.org/doc/219289
ER -

References

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  1. [1] C. Bandle, Isoperimetric Inequalities and Applications, Monographs Stud. Math. 7, Pitman, New York, 1980. Zbl0436.35063
  2. [2] P. Biler, A. Krzywicki and T. Nadzieja, Self-interaction of Brownian particles coupled with thermodynamic processes, Rep. Math. Phys. 42 (1998), 359-372. Zbl1010.82028
  3. [3] Ya. I. Frenkel', Statistical Physics, Izdat. Akad. Nauk SSSR, Moscow, 1948 (in Russian). 
  4. [4] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Grundlehren Math. Wiss. 224, Berlin, 2nd ed., 1983. Zbl0562.35001
  5. [5] M. Grüter and K.-O. Widman, The Green function for uniformly elliptic equations, Manuscripta Math. 37 (1982), 303-342. Zbl0485.35031
  6. [6] A. Krzywicki and T. Nadzieja, Some results concerning the Poisson-Boltzmann equation, Appl. Math. (Warsaw) 21 (1991), 365-272. Zbl0756.35029
  7. [7] C. V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, 1992. Zbl0777.35001
  8. [8] R. F. Streater, A gas of Brownian particles in stochastic dynamics, J. Statist. Phys. 88 (1997), 447-469. Zbl0939.82026

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