On a Nonlinear Problem of the Breaking Water Waves

Настоящая работа посвящена начальной краевой задаче для уравнения Кортевега-де Фриза - Бенджамина - Бона - Махони в конечной области. Эта задача возникает из-за явления длинной волны с малой амплитудой в жидкости. Для некоторых начально-краевых задач для уравнения Кортевега-де Фриза - Бенджамина - Бона - Махони мы получили условия разрушения глобальных решений и решений типа бегущей волны за конечное время. Доказательство результатов основано на методе нелинейной емкости. В заключение мы приводим точные и численные примеры.

Ключевые слова

разрушающие волны; уравнение Кортевега-де Фриза - Бенджамина - Бона - Махони; разрушение решение; начальные граничные задачи.

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