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Controllability of classical solutions implies controllability of weak solutions for a coupled system of wave equations and its application
Authors:Xing Lu
Institution:School of Mathematical Sciences, Fudan University, Shanghai, China
Abstract:In this paper, for a coupled system of one‐dimensional wave equations with Dirichlet boundary controls, we show that the controllability of classical solutions implies the controllability of weak solutions. This conclusion can be applied in proving some results that are hardly obtained by a direct way in the framework of classical solutions. For instance, we strictly derive the necessary conditions for the exact boundary synchronization by two groups in the framework of classical solutions for the coupled system of wave equations. Copyright © 2015 John Wiley & Sons, Ltd.
Keywords:exact boundary controllability  weak solution  classical solution  coupled system of wave equations
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