We study large time asymptotics of solutions to the BBM-Burgers equation ∂t (u - uxx) + βux - μu xx + uux = 0. We are interested in the large time asymptotics for the case, when the initial data have an arbitrary size. Let the initial data u0 ∈ H1 (R) ∩ W1 1 (R), and θ = ∫R u0 (x) dx ≠ 0. Then we prove that there exists a unique solution u(t, x) ∈ C ([0,\∞); H1 (R) ∩ W11 (R) to the Cauchy problem for the BBM-Burgers equation. We also find the large time asymptotics for the solutions.
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