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ArticleOriginal scientific text

Title

A singular radially symmetric problem in electrolytes theory

Authors 1, 2

Affiliations

  1. Institute of Mathematics, Technical University of Zielona Góra, Podgórna 50, 65-246 Zielona Góra, Poland
  2. Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Abstract

Existence of radially symmetric solutions (both stationary and time dependent) for a parabolic-elliptic system describing the evolution of the spatial density of ions in an electrolyte is studied.

Keywords

ENG
radial solutions, electrodiffusion of ions, nonlinear parabolic equation

Bibliography

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  2. [2] P. Biler, W. Hebisch and T. Nadzieja, The Debye system: existence and long time behavior of solutions, ibid. 23 (1994), 1189-1209.
  3. [3] P. Biler and T. Nadzieja, A singular problem in electrolytes theory, Math. Methods Appl. Sci. 20 (1997), 767-782.
  4. [4] P. Biler and T. Nadzieja, Nonlocal parabolic problems in statistical mechanics, Proc. Second World Congress of Nonlinear Analysts, Nonlinear Anal. 30 (1997), 5343-5350.
  5. [5]J. R. Cannon, The One-Dimensional Heat Equation, Addison-Wesley, New York, 1984.
  6. [6]A. Krzywicki and T. Nadzieja, A nonstationary problem in the theory of electrolytes, Quart. Appl. Math. 50 (1992), 105-107.
  7. [7] O. A. Ladyženskaja, V. A. Solonnikov and N. N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc., Providence, R.I., 1988.
  8. [8] T. Nadzieja, A model of radially symmetric cloud of self-attracting particles, Appl. Math. (Warsaw) 23 (1995), 169-178.
  9. [9] M. H. Protter and H. F. Weinberger, Maximum Principles in Differential Equations, Springer, New York, 1984.
  10. [10] I. Rubinstein, Electro-Diffusion of Ions, SIAM Stud. Appl. Math. 11, Philadelphia, 1990.
Applicationes Mathematicae
1998-1999/25/1
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Pages:
101-112
Main language of publication
English
Received
1997-05-08
Published
1998
Exact and natural sciences