Remarks on some nonconservation problems
Abstract: A horizontal channel of uniform cross section has an impervious channel bed to the left of and allows infiltration at a constant rate to the right of . Initially there is water at constant depth and zero velocity. There are left and right moving interfaces and, between them, water with positive velocity. At a certain time there will be a water edge to the right of which there is no water in the channel. The time history of this water edge is a free boundary. The solution of this problem, which is nonconservation because mass and momentum are carried away by infiltration, is discussed below. A single equation, which is also nonconservation, has an explicit solution. The characteristics of this single equation have a geometry similar to that the characteristics of the channel problem.
-  B. Sherman, Free boundaries in one-dimensional flow, Quart. Appl. Math. 41 (1983/84), no. 3, 319–330. MR 721422, https://doi.org/10.1090/S0033-569X-1983-0721422-5
-  B. Sherman, A subsidence problem with free boundary, Proceedings of the Symposium on Free Boundary Problems, Maubuisson-Carcans, France, June 1984, to appear
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