Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

An interface problem: The two-layer shallow water equations

Pages: 5327 - 5345, Volume 33, Issue 11/12, November/December 2013      doi:10.3934/dcds.2013.33.5327

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Madalina Petcu - Laboratoire de Mathématiques et applications, Univ. de Poitiers, Teleport 2 - BP 30179, Boulevard Marie et Pierre Curie, 86962, Futuroscope Chasseneuil Cedex, France (email)
Roger Temam - The Institute for Scientific Computing and Applied Mathematics, Indiana University, 831 East Third Street, Bloomington, Indiana 47405, United States (email)

Abstract: The aim of this article is to study a model of two superposed layers of fluid governed by the shallow water equations in space dimension one. Under some suitable hypotheses the governing equations are hyperbolic. We introduce suitable boundary conditions and establish a result of existence and uniqueness of smooth solutions for a limited time for this model.

Keywords:  Shallow water equations, two layers fluid, transparent boundary conditions, strictly dissipative boundary conditions.
Mathematics Subject Classification:  35L60, 35L65, 35Q35.

Received: September 2011;      Revised: April 2012;      Available Online: May 2013.