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A paper, entitled "Uniform stabilization for the Timoshenko beam by a locallydistributed damping" was published in 2003, in the journal Electronic Journalof Differential Equations. Its title concerns exclusively its Section 3,devoted to the case of equal speeds of propagation and to its main theorem,namely Theorem 3.1. It states that the solutions of the Timoshenko system (see(1.3) in [1]) decays exponentially when the damping coefficient b is locallydistributed. The proof of Theorem 3.1 is crucially based on Lemma 3.6, whichstates the existence of a strict Lyapunov function along which the solutions of(1.3) decay when the speeds of propagation are equal. This rebuttal shows themajor gap and flaws in the proof of Lemma 3.6, which invalidate the proofs ofLemma 3.6 and Theorem 3.1. Lemma 3.6 is stated at the top of page 12. The mainpart of its proof is given in the pages 12 and 13. In the last eight lines ofpage 13, eight inequalities are requested to hold together for the proof ofLemma 3.6. They don't appear in the statements of Lemma 3.6. The subsequentflaws come from the evidence that several of them are contradictory eitherbetween them or with claims in the title of the article. We also point in thisrebuttal other flaws, or gaps in the proofs of Theorem 2.2 related to strongstability and non uniform stability for the case of distinct speeds ofpropagation. In [3], we correct and complete the proof of strong stability. Wealso correct, set up the missing functional frames, fill the gaps in the proofof non uniform stability in the cases of different speeds of propagation, andcomplete a missing argument in the proof of Theorem A in [4] (see Remark 4.3),the result of Theorem A being used in the paper [1] on which this rebuttal ismainly devoted.

Part I: Rebuttal to "Uniform stabilization for the Timoshenko beam by a locally distributed damping"