A singular radially symmetric problem in electrolytes theory

• Autorzy: Tadeusz Nadzieja , Andrzej Raczyński
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

radial solutions; electrodiffusion of ions; nonlinear parabolic equation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1998-1999
• Tom: 25
• Numer: 1
• Strony: 101-112

Daty

wydano

1998

otrzymano

1997-05-08

Twórcy

autor

Tadeusz Nadzieja

• Institute of Mathematics, Technical University of Zielona Góra, Podgórna 50, 65-246 Zielona Góra, Poland

autor

Andrzej Raczyński

• Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Bibliografia

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• [2] P. Biler, W. Hebisch and T. Nadzieja, The Debye system: existence and long time behavior of solutions, ibid. 23 (1994), 1189-1209.
• [3] P. Biler and T. Nadzieja, A singular problem in electrolytes theory, Math. Methods Appl. Sci. 20 (1997), 767-782.
• [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]J. R. Cannon, The One-Dimensional Heat Equation, Addison-Wesley, New York, 1984.
• [6]A. Krzywicki and T. Nadzieja, A nonstationary problem in the theory of electrolytes, Quart. Appl. Math. 50 (1992), 105-107.
• [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] T. Nadzieja, A model of radially symmetric cloud of self-attracting particles, Appl. Math. (Warsaw) 23 (1995), 169-178.
• [9] M. H. Protter and H. F. Weinberger, Maximum Principles in Differential Equations, Springer, New York, 1984.
• [10] I. Rubinstein, Electro-Diffusion of Ions, SIAM Stud. Appl. Math. 11, Philadelphia, 1990.