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In this paper we study the inviscid limit of the Benjamin-Ono-Burgers equation in the energy space H 1/2 (R) or H 1/2 (T). We prove the strong convergence in the energy space of the solution to this equation toward the solution of the Benjamin-Ono equation as the dissipation coefficient converges to 0.doi:10.1090/s0002-9939-2013-11693-x fatcat:24dq4mgvkvbzrajkqz45mmoncu