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Quarterly of Applied Mathematics
  
Online ISSN 1552-4485; Print ISSN 0033-569X
 

Convergence to equilibrium rarefaction waves for discontinuous solutions of shallow water wave equations with relaxation


Authors: Haitao Fan and Tao Luo
Journal: Quart. Appl. Math. 63 (2005), 575-600
MSC (2000): Primary 35L65, 35L67, 35L60
Published electronically: August 18, 2005
MathSciNet review: 2169035
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Abstract: The purpose of this paper is to study the discontinuous solutions to a shallow water wave equation with relaxation. The typical initial value problem of discontinuous solutions is the Riemann problem. Unlike the homogeneous hyperbolic conservation laws, due to the inhomogeneity of the system studied here, the solutions of the Riemann problem do not have a self-similar structure anymore. This problem can be formulated as a free boundary problem. We show that the Riemann solutions still have a piecewise smooth structure globally and converge to the rarefaction waves of the equilibrium equation as time tends to infinity.


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Additional Information

Haitao Fan
Affiliation: Department of Mathematics, Georgetown University, Washington, DC 20057-1233
Email: fanh@georgetown.edu

Tao Luo
Affiliation: Department of Mathematics, Georgetown University, Washington, DC 20057-1233
Email: tl48@georgetown.edu

DOI: http://dx.doi.org/10.1090/S0033-569X-05-00980-4
PII: S 0033-569X(05)00980-4
Keywords: Shallow water wave equations, relaxation, shock waves, rarefaction waves, free boundary problem
Received by editor(s): February 10, 2005
Published electronically: August 18, 2005
Article copyright: © Copyright 2005 Brown University
The copyright for this article reverts to public domain 28 years after publication.



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