Non-homogeneous boundary value problems for the Korteweg-de Vries and the Korteweg-de Vries-Burgers equations in a quarter plane

@inproceedings{Bona2008NonhomogeneousBV,
  title={Non-homogeneous boundary value problems for the Korteweg-de Vries and the Korteweg-de Vries-Burgers equations in a quarter plane},
  author={Jerry L. Bona and Shu-Ming Sun and Bing-Yu Zhang},
  year={2008}
}
Attention is given to the initial-boundary-value problems (IBVPs) ut + ux + uux + uxxx = 0, for x, t ≥ 0, u(x, 0) = φ(x), u(0, t) = h(t)  (0.1) for the Korteweg-de Vries (KdV) equation and ut + ux + uux − uxx + uxxx = 0, for x, t ≥ 0, u(x, 0) = φ(x), u(0, t) = h(t)  (0.2) for the Korteweg-de Vries-Burgers (KdV-B) equation. These type of problems arise in modeling waves generated by a wavemaker in a channel and waves incoming from deep water into near-shore zones (see [2] and [5] for… CONTINUE READING
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