Смешанная задача для линейного дифференциального уравнения параболического типа с нелинейными импульсными условиями
https://doi.org/10.17586/2220-8054-2024-15-2-160-169
Аннотация
В данной работе в пространстве обобщенных функций рассматривается линейное уравнение в частных производных параболического типа как уравнение диффузии нейтронов при наличии поглощения нейтронов атомным ядром с нелинейными импульсными эффектами. С помощью краевых условий Дирихле получена спектральная задача и исследована эта проблема. Применен метод Фурье разделения переменных. Получена счетная система нелинейных функционально-интегральных уравнений относительно коэффициентов Фурье неизвестной функции. Доказана теорема об однозначной разрешимости счетной системы функциональных интегральных уравнений. Метод последовательных приближений используется в сочетании с методом сжимающего отображения. Получены критерии единственности и существования обобщенного решения импульсной смешанной задачи. Решение смешанной задачи получено в виде ряда Фурье. Доказана равномерная сходимость рядов Фурье.
Об авторах
Т. К. Юлдашев
Tashkent State University of Economics
Узбекистан
Узбекистан
А. K. Файзиев
Tashkent State University of Economics
Узбекистан
Узбекистан
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Рецензия
Для цитирования:
Юлдашев Т.К., Файзиев А.K. Смешанная задача для линейного дифференциального уравнения параболического типа с нелинейными импульсными условиями. Наносистемы: физика, химия, математика. 2024;15(2):160-169. https://doi.org/10.17586/2220-8054-2024-15-2-160-169
For citation:
Yuldashev T.K., Fayziyev A.K. Mixed problem for a linear differential equation of parabolic type with nonlinear impulsive conditions. Nanosystems: Physics, Chemistry, Mathematics. 2024;15(2):160-169. https://doi.org/10.17586/2220-8054-2024-15-2-160-169
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