The Exact Boundary Controllability of Nodal Profile for Entropy Solutions to 1-D Quasilinear Hyperbolic Systems of Conservation Laws with Linearly Degenerate Negative (Resp., Positive) Characteristic Fields

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Abstract. We consider the exact boundary controllability of nodal profile for entropy solutions to 1-D quasilinear hyperbolic systems of conservation laws [Formula: see text] under the assumption that all negative (resp., positive) characteristic fields are linearly degenerate. We prove that for small initial-boundary data, if the total variations of the nodal profile and the boundary data given at [Formula: see text] (resp., [Formula: see text]) are sufficiently small, then there exists a time [Formula: see text] and boundary controls at [Formula: see text] (resp., [Formula: see text]), such that the corresponding mixed initial-boundary value problem admits a unique entropy solution as the limit of front tracking approximate solutions, which takes the given nodal profile at the boundary [Formula: see text] (resp., [Formula: see text]) from a time larger than [Formula: see text] to infinity. Moreover, if the nodal profile decays to zero when [Formula: see text], then the entropy solution, together with the boundary control, possesses the same decay rate as the nodal profile.

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