We consider the problem of boundary stabilization of a particular class of systems of conservation laws. Precisely, 2x2 systems with positive characteristic speeds are under view. We study boundary controls in the form of a linear feedback, and give sufficient conditions on the control law to stabilize the system. The main contribution is that we consider weak entropy solutions for this system while most of the results concerning the boundary stabilization of systems of conservation consider continuously differentiable solutions. This is a joint work with J.-M. Coron, S. Ervedoza, S. Goshal and V. Perrollaz.

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