An interface problem: The two-layer shallow water equations

Madalina Petcu; Roger Temam

doi:10.3934/dcds.2013.33.5327

Article Contents

2013, Volume 33, Issue 11&12: 5327-5345. Doi: 10.3934/dcds.2013.33.5327

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An interface problem: The two-layer shallow water equations

Madalina Petcu^1, and
Roger Temam^2,

1.
Laboratoire de Mathématiques et applications, Univ. de Poitiers, Teleport 2 - BP 30179, Boulevard Marie et Pierre Curie, 86962, Futuroscope Chasseneuil Cedex
2.
The Institute for Scientific Computing and Applied Mathematics, Indiana University, 831 East Third Street, Bloomington, Indiana 47405

Received: August 31, 2011

Revised: March 31, 2012

Published: October 2013

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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.

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