Abstract.
We study large time asymptotics of solutions to the BBM–Burgers equation
. We are interested in the large time asymptotics for the case, when the initial data have an arbitrary size. Let the initial data \(u_{0} \in {\bf H}^{1} ({\bf R}) \cap {\bf W}^{1}_{1} ({\bf R})\), and \(\theta = \int _{\bf R} u_{0} (x) dx \neq 0\). Then we prove that there exists a unique solution \(u (t, x) \in {\bf C} ([0,\infty); {\bf H}^{1} ({\bf R}) \cap {\bf W}^{1}_{1} ({\bf R}))\) to the Cauchy problem for the BBM–Burgers equation. We also find the large time asymptotics for the solutions
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Communicated by Rafael D. Benguria.
To the memory of Professor Tsutomu Arai
Submitted: February 5, 2006. Accepted: June 17, 2006.
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Hayashi, N., Kaikina, E.I. & Naumkin, P.I. Large Time Asymptotics for the BBM–Burgers Equation. Ann. Henri Poincaré 8, 485–511 (2007). https://doi.org/10.1007/s00023-006-0314-4
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DOI: https://doi.org/10.1007/s00023-006-0314-4