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Матем. сб., 1970, том 81(123), номер 2, страницы 228–255 (Mi msb3372)  

Эта публикация цитируется в 549 научных статьях (всего в 550 статьях)

Квазилинейные уравнения первого порядка со многими независимыми переменными

С. Н. Кружков


Аннотация: В работе построена теория обобщенных решений задачи Коши в целом для уравнений
$$ u_t+\sum_{i=1}^n\frac d{dx_i}\varphi_i(t,x,u)+\psi(t,x,u)=0 $$
в классе ограниченных измеримых функций. Дано определение обобщенного решения и доказаны теоремы существования, единственности и устойчивости такого решения. Для доказательства теоремы существования применен “метод исчезающей вязкости”; в связи с этим предварительно изучается задача Коши для соответствующего параболического уравнения и для решения этой задачи устанавливаются априорные оценки модуля непрерывности в $L_1$, не зависящие от малой вязкости.
Библиография: 22 названия.

Полный текст: PDF файл (2638 kB)
Список литературы: PDF файл   HTML файл

Англоязычная версия:
Mathematics of the USSR-Sbornik, 1970, 10:2, 217–243

Реферативные базы данных:

УДК: 517.944
MSC: 35K45, 35A05, 26A42
Поступила в редакцию: 23.04.1969

Образец цитирования: С. Н. Кружков, “Квазилинейные уравнения первого порядка со многими независимыми переменными”, Матем. сб., 81(123):2 (1970), 228–255; S. N. Kruzhkov, “First order quasilinear equations in several independent variables”, Math. USSR-Sb., 10:2 (1970), 217–243

Цитирование в формате AMSBIB
\RBibitem{Kru70}
\by С.~Н.~Кружков
\paper Квазилинейные уравнения первого порядка со многими независимыми переменными
\jour Матем. сб.
\yr 1970
\vol 81(123)
\issue 2
\pages 228--255
\mathnet{http://mi.mathnet.ru/msb3372}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=267257}
\zmath{https://zbmath.org/?q=an:0202.11203|0215.16203}
\transl
\by S.~N.~Kruzhkov
\paper First order quasilinear equations in several independent variables
\jour Math. USSR-Sb.
\yr 1970
\vol 10
\issue 2
\pages 217--243
\crossref{https://doi.org/10.1070/SM1970v010n02ABEH002156}


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