### Abstract

We study the following initial-boundary value problem for the Korteweg-de Vries-Burgers equation equation presented We prove that if the initial data u_{0} ∈ H^{0,ω} ∩ H^{0,ω}, where ω ∈ (1/2, 3/2), then there exists a unique solution u ∈ C ([0,∞), H^{1,ω}) of the initial-boundary value problem (0.1). Moreover if the initial data are such that x^{1+μ}u_{0}(x) ∈ L^{1}, μ = ω - 1/2, then there exists a constant A such that the solution has the following asymptotics equation presented for t → ∞ uniformly with respect to x > 0.

Original language | English |
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Pages (from-to) | 319-347 |

Number of pages | 29 |

Journal | Journal of Evolution Equations |

Volume | 2 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2002 Dec 1 |

Externally published | Yes |

### Keywords

- Dissipative Nonlinear Evolution Equation
- Korteweg-de Vries-Burgers equation
- Large Time Asymptotics

### ASJC Scopus subject areas

- Mathematics (miscellaneous)

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## Cite this

Hayashi, N., Kaikina, E. I., & Ruiz Paredes, H. F. (2002). Korteweg-de Vries-Burgers equation on a half-line with large initial data.

*Journal of Evolution Equations*,*2*(3), 319-347. https://doi.org/10.1007/s00028-002-8091-0