The steady state of the Chapman-Ferraro problem is formulated in mathematical terms, but the three-dimensional problem presents little hope of an analytical solution, and it is not even obvious how to compute the solution. The two-dimensional problem is reduced to a standard potential problem and solved exactly. The solution is used to obtain an indication of the error in the flat-faced approximate model that has been used previously in three dimensions.
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J. W. Dungey (1961) studied this question.
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