2 RELATED FREE-BOUNDARY PROBLEMS

Two related free boundary problems are solved: the first is the viscou s film coating of wedges of arbitrary angle; the second is the rectang ular dam problem with evaporation (or fluid removal) from the free sur face. Both problems are of practical interest and explicit solutions a re given. The two examples treated are generalizations of problems sol ved using Polubarinova-Kochina's (1962) analytic differential equation method and conformal mappings involving elliptic modular functions to an intermediate plane. Here conformal mappings involving Legendre fun ctions are used to generalize these results.