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

Nadzieja, Tadeusz; Raczyński, Andrzej

Applicationes Mathematicae, Tome 27 (2000), p. 465-473 / Harvested from The Polish Digital Mathematics Library

Résumé

We consider the following problem: $Δ Φ = \pm M ο v e r \int_{Ω} e^{- Φ / Θ} e^{- Φ / Θ}, E = M Θ \mp 1 ο v e r 2 \int_{Ω} {| \nabla Φ |}^{2} {, Φ |}_{\partial Ω} = 0,$ where Φ: Ω ⊂ $ℝ^{n}$ → ℝ is an unknown function, Θ is an unknown constant and M, E are given parameters.

Publié le : 2000-01-01

Zbl 0992.35041

EUDML-ID : urn:eudml:doc:219289

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     author = {Tadeusz Nadzieja and Andrzej Raczy\'nski},
     title = {Radially symmetric solutions of the Poisson-Boltzmann equation with a given energy},
     journal = {Applicationes Mathematicae},
     volume = {27},
     year = {2000},
     pages = {465-473},
     zbl = {0992.35041},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv27i4p465bwm}
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Nadzieja, Tadeusz; Raczyński, Andrzej. Radially symmetric solutions of the Poisson-Boltzmann equation with a given energy. Applicationes Mathematicae, Tome 27 (2000) pp. 465-473. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv27i4p465bwm/

Bibliographie

[000] [1] C. Bandle, Isoperimetric Inequalities and Applications, Monographs Stud. Math. 7, Pitman, New York, 1980. | Zbl 0436.35063

[001] [2] P. Biler, A. Krzywicki and T. Nadzieja, Self-interaction of Brownian particles coupled with thermodynamic processes, Rep. Math. Phys. 42 (1998), 359-372. | Zbl 1010.82028

[002] [3] Ya. I. Frenkel', Statistical Physics, Izdat. Akad. Nauk SSSR, Moscow, 1948 (in Russian).

[003] [4] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Grundlehren Math. Wiss. 224, Berlin, 2nd ed., 1983. | Zbl 0562.35001

[004] [5] M. Grüter and K.-O. Widman, The Green function for uniformly elliptic equations, Manuscripta Math. 37 (1982), 303-342. | Zbl 0485.35031

[005] [6] A. Krzywicki and T. Nadzieja, Some results concerning the Poisson-Boltzmann equation, Appl. Math. (Warsaw) 21 (1991), 365-272. | Zbl 0756.35029

[006] [7] C. V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, 1992. | Zbl 0777.35001

[007] [8] R. F. Streater, A gas of Brownian particles in stochastic dynamics, J. Statist. Phys. 88 (1997), 447-469. | Zbl 0939.82026