Geodesic
Exact solutions of two limiting quasistationary electrochemical shaping
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2011), pp. 21-29

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We model the precision electrochemical machining with the help of a jump-like current efficiency function, assuming that in the working area of the machined surface the current density takes on the critical value. We formulate and solve limiting quasistationary shaping problems, which allows us to study a nonstationary process with sufficient accuracy.
Keywords: nonstationary Hele–Shaw problem, quasistationary approximation, analytic functions, conformal mapping. 
@article{IVM_2011_12_a2,
     author = {V. P. Zhitnikov and E. M. Oshmarina and G. I. Fedorova},
     title = {Exact solutions of two limiting quasistationary electrochemical shaping},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {21--29},
     publisher = {mathdoc},
     number = {12},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_12_a2/}
}
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V. P. Zhitnikov; E. M. Oshmarina; G. I. Fedorova. Exact solutions of two limiting quasistationary electrochemical shaping. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2011), pp. 21-29. http://geodesic.mathdoc.fr/item/IVM_2011_12_a2/