A free boundary problem involving a cusp. II: local analysis
Hans Wilhelm Alt, C.J. van Duijn · TU/e Research Portal · 1998
Absti•act.We consider a sta.tionary free boundary problem deseribing the stationary flow of fresh and salt water in a porous medium.The salt water is supposed to lw. fib:1gnant: whih•.' the fresh water on top of it is drawn into wells.In a. previous work it has been shown, that for pumping rates Q < Qc,. a solution with smooth interface exists.In thiH part Wt:~ study the case Q = Qc.,. in two dimensions; vVe show that the interface has isolated singularities.At eac:h singularity the free boundary develops a. cusp or becomes vertical.By mt.~ans of local ana.ly:;;istechniques we obta.in the asymptotic: behaviour of the fo7.