Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Remarks on some nonconservation problems

Author: B. Sherman
Journal: Quart. Appl. Math. 44 (1986), 313-318
MSC: Primary 76B15
DOI: https://doi.org/10.1090/qam/856185
MathSciNet review: 856185
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Abstract: A horizontal channel of uniform cross section has an impervious channel bed to the left of $ x = 0$ and allows infiltration at a constant rate to the right of $ x = 0$. 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 $ {C_2}$ characteristics of the channel problem.

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DOI: https://doi.org/10.1090/qam/856185
Article copyright: © Copyright 1986 American Mathematical Society

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