We study unique continuation properties of solutions to the b-family of equations. This includes the Camassa-Holm and the Degasperi-Procesi models. We prove that for both, the initial value problem and the periodic boundary value problem, the unique continuation results found in {LiPo} are optimal. More precisely, the result established there for the constant c₀=0 fails for any constant c₀≠ 0.
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Hong et al. (2024) studied this question.
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