On a Nonlinear Problem of the Breaking Water Waves
DOI:
https://doi.org/10.14529/mmp190203Keywords:
breaking waves, Korteweg-de Vries–Benjamin–Bona–Mahony equation, blow-up of solution, initial-boundary problems.Abstract
The paper is devoted to the initial boundary value problem for the Korteweg-de Vries– Benjamin–Bona–Mahony equation in a finite domain. This particular problem arises from the phenomenon of long wave with small amplitude in fluid. For certain initial-boundary problems for the Korteweg-de Vries–Benjamin–Bona–Mahony equation, we obtain the conditions of blowing-up of global and travelling wave solutions in finite time. The proof of the results is based on the nonlinear capacity method. In closing, we provide the exact and numerical examples.References
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