Preprint 2004-011

Global Structure and Asymptotic Behavior of Weak Solutions to Flood Wave Equations

Tao Luo and Tong Yang

Abstract: The present paper concerns with the global structure and asymptotic behavior of the discontinuous solutions to flood wave equations. By solving a free boundary problem, we first obtain the global structure and large time behavior of the weak solutions containing two shock waves. For the Cauchy problem with a class of initial data, we use Glimm scheme to obtain a uniform BV estimate both with respect to time and the relaxation parameter. This yields the global existence of BV solution and convergence to the equilibrium equation as the relaxation parameter tends to 0.

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Tao Luo, <>
Tong Yang, <>
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<> March 21 2004.

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