Классическое решение первой смешанной задачи для слабоквазилинейного волнового уравнения: метод неподвижной точки
https://doi.org/10.67268/1812-5093-2026-34-1-85-95
EDN: DCQCNW
Аннотация
Для одномерного слабо квазилинейного волнового уравнения, заданного в первом квадранте, рассматривается смешанная задача, в которой на пространственной полуоси задаются условия Коши, а на временной полуоси задается условие Дирихле. Нелинейность содержит независимые переменные, искомую функцию и ее производные. Решение строится в неявном аналитическом виде как решение некоторых интегро-дифференциальных уравнений. Разрешимость интегро-дифференциальных уравнений доказывается с использованием обобщения теоремы Банаха о неподвижной точке. Для рассматриваемой задачи доказывается единственность решения и устанавливаются условия, при выполнении которых существует ее классическое решение.
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Рецензия
Для цитирования:
Рудько Я.В. Классическое решение первой смешанной задачи для слабоквазилинейного волнового уравнения: метод неподвижной точки. Труды Института математики НАН Беларуси. 2026;34(1):85-95. https://doi.org/10.67268/1812-5093-2026-34-1-85-95. EDN: DCQCNW
For citation:
Rudzko J.V. Classical solution to the first mixed problem for a mildly quasilinear wave equation: a fixed-point approach. Proceedings of the Institute of Mathematics of the NAS of Belarus. 2026;34(1):85-95. https://doi.org/10.67268/1812-5093-2026-34-1-85-95. EDN: DCQCNW
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