### Abstract

We study large time asymptotics of solutions to the BBM-Burgers equation ∂_{t} (u - u_{xx}) + βu_{x} - μu _{xx} + uu_{x} = 0. 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} ∈ H^{1} (R) ∩ W_{1} ^{1} (R), and θ = ∫_{R} u_{0} (x) dx ≠ 0. Then we prove that there exists a unique solution u(t, x) ∈ C ([0,\∞); H^{1} (R) ∩ W_{1}^{1} (R) to the Cauchy problem for the BBM-Burgers equation. We also find the large time asymptotics for the solutions.

Original language | English |
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Pages (from-to) | 485-511 |

Number of pages | 27 |

Journal | Annales Henri Poincare |

Volume | 8 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2007 Jun |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Nuclear and High Energy Physics
- Mathematical Physics

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## Cite this

Hayashi, N., Kaikina, E. I., & Naumkin, P. I. (2007). Large time asymptotics for the BBM-burgers equation.

*Annales Henri Poincare*,*8*(3), 485-511. https://doi.org/10.1007/s00023-006-0314-4