The focus of the current paper is the higher order nonlinear dispersive equation which models unidirectional propagation of small amplitude long waves in dispersive media. The specific interest is in the initial-boundary value problem where spatial variable lies in R+; namely, quarter plane problem. With proper requirement on initial and boundary condition, we show local and global well posedness.
Bibliographical noteKAUST Repository Item: Exported on 2022-06-03
Acknowledgements: The author wishes to record her thanks to the Archimedes Center for Modeling, Analysis and Computation at the University of Crete, Greece and University of Illinois at Chicago for support and hospitality during an early and important stage of this research. She received support from Universit´e ParisEst Cr´eteil-Val de Marne (ex-Universit´e Paris 12). The paper is finished when she was visiting King Abdullah University of Science and Technology in Kingdom of Saudi Arabia and Mathematic Division of National Center for Theoretical Science at National Taiwan University.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.