Boundary Value Problem for Third Order Partial Integro-Differential Equation with a Degenerate Kernel

Yuldashev, T. K.; Apakov, Yu. P.; Zhuraev, A. Kh.

doi:10.1134/s1995080221060329

Cited by 21 publications

(4 citation statements)

References 19 publications

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“…Problems with nonlocal conditions for differential and integro-differential equations are considered in the large number of publications, such as . In [30][31][32][33][34][35][36], integro-differential equations with a degenerate kernel were considered. In the present paper, we study the solvability of the inverse problem for a hyperbolic type partial integro-differential equation with a degenerate kernel, three parameters, final conditions at the end of the interval and involution.…”

Section: Problem Statementmentioning

confidence: 99%

Inverse Problem for a Hyperbolic Integro-Differential Equation with two Redeﬁnition Conditions at the End of the Interval and Involution

Yuldashev,

Kilichev

2024

Az. J. Math.

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In this paper, we consider an inhomogeneous hyperbolic type partial integrodifferential equation with degenerate kernel, two redefinition functions and involution. Intermediate data are used to find these redefinition functions. Dirichlet boundary conditions with respect to spatial variable are used. The Fourier method of separation of variables is applied. The countable system of functional-integral equations is obtained. Theorem on a unique solvability of countable system of functional-integral equations is proved. The method of successive approximations is used in combination with the method of contraction mappings. The triple of solutions of the inverse problem is obtained in the form of Fourier series. Absolute convergence of Fourier series is proved.

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Section: Problem Statementmentioning

confidence: 99%

Inverse Problem for a Hyperbolic Integro-Differential Equation with two Redeﬁnition Conditions at the End of the Interval and Involution

Yuldashev,

Kilichev

2024

Az. J. Math.

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“…Найдем собственные значения и собственные функции задачи (9). Положим (10) Подставляя (10) в уравнение (9), разделяя переменные, имеем задачи…”

Section: Y Z U D Y Z Dydz U Y Z U Y Z Dydz U D Y Z Dydzunclassified

“…Дифференциальные уравнения в частных производных третьего порядка рассматриваются при решении задач теории нелинейной акустики и в гидродинамической теории космической плазмы, фильтрации жидкости в пористых средах. Дифференциальные уравнения в частных производных третьего порядка изучаются многими авторами (см., например, [1][2][3][4][5][6][7][8][9][10][11]).…”

Section: Introductionunclassified

О Разрешимости Краевой Задачи Для Уравнения Третьего Порядка С Кратными Характеристиками В Трехмерном Пространстве В Полуограниченной Области

Апаков,

Хамитов

2023

ВОГУМФТ

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В работе для уравнения третьего порядка с кратными характеристиками рассмотрена краевая задача в трехмерном пространстве в полуограниченной области. Единственность решения поставленной задачи доказана методом интегралов энергии. Существование решения доказано методом разделения переменных. Решение построено явно в виде бесконечного ряда, обоснована возможность почленного дифференцирования ряда по всем переменным.

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“…Problems with nonlocal conditions for differential and integro-differential equations were considered in . Integro-differential equations with degenerate kernel were considered in [36][37][38][39][40].…”

Section: Problem Statementmentioning

confidence: 99%

Inverse problem for Fredholm integro-differential equation with final redefinition conditions at the end of the interval

Yuldashev¹,

Zarifzoda²

2022

Nanosystems: Phys. Chem. Math.

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The questions of solvability and construction of solutions of an inverse problem for second-order Fredholm integro-differential equation with degenerate kernel, final conditions at the end of the interval, two parameters, and two redefinition data are considered. The sets of regular parameter values are determined and the corresponding solutions are constructed. The specific features of the inverse problem are studied. Criteria for the unique solvability of the posed inverse problem are established. KEYWORDS integro-differential equation, degenerate kernel, final conditions at the end of a segment, parameters, redefinition data, solvability.

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Boundary Value Problem for Third Order Partial Integro-Differential Equation with a Degenerate Kernel

Cited by 21 publications

References 19 publications

Inverse Problem for a Hyperbolic Integro-Differential Equation with two Redeﬁnition Conditions at the End of the Interval and Involution

Inverse Problem for a Hyperbolic Integro-Differential Equation with two Redeﬁnition Conditions at the End of the Interval and Involution

О Разрешимости Краевой Задачи Для Уравнения Третьего Порядка С Кратными Характеристиками В Трехмерном Пространстве В Полуограниченной Области

Inverse problem for Fredholm integro-differential equation with final redefinition conditions at the end of the interval

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