Some Isoperimetric Inequalities in Electrochemistry and Hele Shaw Flows |
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Authors: | GUSTAFSSON BJ?RN; MOSSINO JACQUELINE |
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Institution: |
Department of Mathematics, Royal Institute of Technology S-100 44 Stockholm 70, Sweden
Laboratoire d'Analyse Num?rique, CNRS et Universit? Paris-Sud Batiment 425, 91405 Orsay, France
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Abstract: | Isoperimetric inequalities are applied to a moving-boundaryproblem for doubly-connected domains. This problem occurs forexample in electrochemistry, in which case the domains in questionare the electrolyte of an electrolytic cell. The two electrodessurrounding the electrolyte are assumed to grow or dissolve,at different rates in general, by electrochemical reaction.We obtain optimal estimates showing, for example, that the leastchange in volume of each electrode always occurs in sphericalsymmetry. |
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