Geodesic
On a nonlinear electrolysis problem
Sbornik. Mathematics, Tome 82 (1995) no. 1, pp. 87-99

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A mathematical model proposed by H. Amann for electrochemical reactions is considered. The model is considered in the steady-state case for two differently charged components of a solution. In this case the model reduces to a quasilinear system of two elliptic equations with nonlinear Neumann boundary conditions. In the regular case it is proved that this nonlinear problem is globally solvable in a Sobolev space $W_p^2(\Omega)$ with $p>n$ ($\Omega\subset\mathbb{R}^n$). 
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     author = {S. I. Pokhozhaev},
     title = {On a nonlinear electrolysis problem},
     journal = {Sbornik. Mathematics},
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     number = {1},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_82_1_a3/}
}
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S. I. Pokhozhaev. On a nonlinear electrolysis problem. Sbornik. Mathematics, Tome 82 (1995) no. 1, pp. 87-99. http://geodesic.mathdoc.fr/item/SM_1995_82_1_a3/