Abstract
In this paper, we consider the asymptotic stability of the exact boundary controllability of nodal profile for 1D quasi‐linear wave equations. First, for 1D quasi‐linear hyperbolic systems with zero eigenvalues, we establish the existence and uniqueness of semiglobal classical solution to the one‐sided mixed initial‐boundary value problem on a semibounded initial axis and discuss the asymptotic behavior of the corresponding solutions under different hypotheses on the initial data. Based on these results, we obtain the asymptotic stability of the exact boundary controllability of nodal profile for 1D quasi‐linear wave equations on a semibounded time interval.
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