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

The one dimensional shallow water equations with Dirichlet boundary conditions on the velocity

Pages: 209 - 222, Volume 4, Issue 1, February 2011      doi:10.3934/dcdss.2011.4.209

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Madalina Petcu - Laboratoire de Mathématiques et Applications UMR CNRS 6086, Université de Poitiers, Téléport 2 - BP 30179, Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil, France (email)
Roger Temam - The Institute for Scientific Computing and Applied Mathematics, Indiana University, 831 E. 3rd St., Rawles Hall, Bloomington, IN 47405, United States (email)

Abstract: In the present article we consider the nonviscous Shallow Water Equations in space dimension one with Dirichlet boundary conditions for the velocity and we show the locally in time well-posedness of the model.

Keywords:  a priori estimates, shallow water, well posedness.
Mathematics Subject Classification:  35A07, 35B45, 35F30, 35L60.

Received: June 2009;      Revised: September 2009;      Available Online: October 2010.