Skip to Main Content
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 76B15

Retrieve articles in all journals with MSC: 76B15


Additional Information

Article copyright: © Copyright 1986 American Mathematical Society