Two related free boundary problems |
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| Authors: | CRASTER R. V. |
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| Affiliation: | Department of Applied Mathematics and Theoretical Physics, University of Cambridge Cambridge CB3 9EW, UK |
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| Abstract: | Two related free boundary problems are solved: the first isthe viscous film coating of wedges of arbitrary angle; the secondis the rectangular dam problem with evaporation (or fluid removal)from the free surface. Both problems are of practical interestand explicit solutions are given. The two examples treated aregeneralizations of problems solved using Polubarinova-Kochina's(1962) analytic differential equation method and conformal mappingsinvolving elliptic modular functions to an intermediate plane.Here conformal mappings involving Legendre functions are usedto generalize these results. |
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