Mixed problems for the Korteweg-de Vries equation

Results are established concerning the non-local solubility and well posedness in various function spaces of the mixed problem for the Korteweg-de Vries equation u(t) + u(xxx) + au(x) + uu(x) = f(t, x) in the half-strip (0,T) x (-infinity,0). Some a priori estimates of the solutions are obtained using a special solution J(t, x) of the linearized Kdv equation of boundary potential type. Properties of J are studied which differ essentially as x --> +infinity or x --> -infinity. Application of this boundary potential enables us in particular to prove the existence of generalized solutions with non-regular boundary values.

Авторы
Редакторы
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Журнал
Издательство
Russian Academy of Sciences
Номер выпуска
5-6
Язык
Английский
Страницы
903-935
Статус
Опубликовано
Подразделение
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Ссылка
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Номер
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Том
190
Год
1999
Организации
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Ключевые слова
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Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/9211/