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.
@article{bwmeta1.element.bwnjournal-article-zmv25i1p101bwm, author = {Tadeusz Nadzieja and Andrzej Raczy\'nski}, title = {A singular radially symmetric problem in electrolytes theory}, journal = {Applicationes Mathematicae}, volume = {25}, year = {1998}, pages = {101-112}, zbl = {0919.35020}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv25i1p101bwm} }
Nadzieja, Tadeusz; Raczyński, Andrzej. A singular radially symmetric problem in electrolytes theory. Applicationes Mathematicae, Tome 25 (1998) pp. 101-112. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv25i1p101bwm/
[000] [1] P. Biler, Existence and asymptotics of solutions for a parabolic-elliptic system with nonlinear no-flux boundary conditions, Nonlinear Anal. 19 (1992), 1121-1136. | Zbl 0781.35025
[001] [2] P. Biler, W. Hebisch and T. Nadzieja, The Debye system: existence and long time behavior of solutions, ibid. 23 (1994), 1189-1209. | Zbl 0814.35054
[002] [3] P. Biler and T. Nadzieja, A singular problem in electrolytes theory, Math. Methods Appl. Sci. 20 (1997), 767-782. | Zbl 0885.35051
[003] [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. | Zbl 0892.35073
[004] [5]J. R. Cannon, The One-Dimensional Heat Equation, Addison-Wesley, New York, 1984. | Zbl 0567.35001
[005] [6]A. Krzywicki and T. Nadzieja, A nonstationary problem in the theory of electrolytes, Quart. Appl. Math. 50 (1992), 105-107. | Zbl 0754.35142
[006] [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.
[007] [8] T. Nadzieja, A model of radially symmetric cloud of self-attracting particles, Appl. Math. (Warsaw) 23 (1995), 169-178. | Zbl 0839.35110
[008] [9] M. H. Protter and H. F. Weinberger, Maximum Principles in Differential Equations, Springer, New York, 1984.
[009] [10] I. Rubinstein, Electro-Diffusion of Ions, SIAM Stud. Appl. Math. 11, Philadelphia, 1990.