Quarterly of Applied Mathematics

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

Author(s): Haitao Fan; Tao Luo
Journal: Quart. Appl. Math. 63 (2005), 575-600.
MSC (2000): Primary 35L65, 35L67, 35L60
Posted: August 18, 2005
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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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Retrieve articles in Quarterly of Applied Mathematics with MSC (2000): 35L65, 35L67, 35L60

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

PII: S0033-569X-05-00980-4
Keywords: Shallow water wave equations, relaxation, shock waves, rarefaction waves, free boundary problem
Received by editor(s): February 10, 2005
Posted: August 18, 2005
Copyright of article: Copyright 2005, Brown University
The copyright for this article reverts to public domain after 28 years from publication.

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