Convergence of the Successive Approximation Method in the Cauchy Problem for an Integro-Differential Equation with Quadratic Nonlinearity

V. L. Vaskevich, A. I. Shcherbakov

Результат исследования: Научные публикации в периодических изданияхстатья

2 Цитирования (Scopus)

Аннотация

The equations considered in this article have the form in which the time derivative of the unknown function is expressed as a double integral over the space variables of a weighted quadratic expression of the sought function. The domain of integration is unbounded and does not depend on time but depends on the space variable. We study the Cauchy problem in the function classes accompanying the equation with initial data on the positive half-line. In application to this problem, the convergence of the successive approximation method is justified. An estimate is given of the quality of the approximation depending on the number of the iterated solution. It is proved that, on any finite time interval, the posed Cauchy problem has at most one solution in the accompanying function class. An existence theorem is proved in the same class.

Язык оригиналаанглийский
Страницы (с-по)128-136
Число страниц9
ЖурналSiberian Advances in Mathematics
Том29
Номер выпуска2
DOI
СостояниеОпубликовано - 1 апр 2019

Fingerprint Подробные сведения о темах исследования «Convergence of the Successive Approximation Method in the Cauchy Problem for an Integro-Differential Equation with Quadratic Nonlinearity». Вместе они формируют уникальный семантический отпечаток (fingerprint).

  • Цитировать