A generalized integral problem for a system of hyperbolic equations and its applications

Assanova, A. T.

doi:10.15672/hujms.1094454

Cited by 3 publications

(1 citation statement)

References 25 publications

(35 reference statements)

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“…involving impulsive effects and delayed arguments [17][18][19], and addressing systems of hyperbolic equations with loads and piecewise-constant arguments [20][21][22][23][24].…”

Section: Introduction and Statement Of Problemmentioning

confidence: 99%

On a non-local problem for system of partial differential equations of hyperbolic type in a specific domain

Assanova

2023

ijmph

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The non-local problem for second order system of partial differential equations of hyperbolic type is studied in the specific domain. For solving this problem we use a functional parametrization method. This method is an extension of Dzhumabaev's parametrization method to a partial differential equations of hyperbolic type. We introduce a parameter-function, expressed as the unknown function's value at the characteristics 𝑡𝑡𝑡𝑡 = 0 within the given domain. This transforms the nonlocal problem into an equivalent parameterized problem, involving the Goursat problem for a system of partial differential equations of hyperbolic type and an additional relation based on the functional parameter. Subsequently, starting from the additional condition and the consistency condition, we formulate the Cauchy problem for a system of differential equations with respect to the unknown parameter-function. We develop an algorithm for solving the parameterized problem and demonstrate its convergence. Additionally, we derive conditions for the existence and uniqueness of a solution to the parameterized problem. Unique solvability conditions for the nonlocal problem for second-order system of partial differential equations of hyperbolic type in a specific domain are established in terms of the initial data.

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“…involving impulsive effects and delayed arguments [17][18][19], and addressing systems of hyperbolic equations with loads and piecewise-constant arguments [20][21][22][23][24].…”

Section: Introduction and Statement Of Problemmentioning

confidence: 99%

On a non-local problem for system of partial differential equations of hyperbolic type in a specific domain

Assanova

2023

ijmph

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Построение Решения В Широком Смысле Линейной Счетной Системы Дифференциальных Уравнений

Курмангалиев,

Бекбауова

2024

BULLETIN Series of Physics &Amp; Mathematical Sciences

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В статье рассматриваются вопросы существования и единственностипериодических по некоторым переменным решений в широком смысле для счетных систем в частных производных. Изучение периодических решений систем дифференциальных уравнений имеет важное значение в современной теории дифференциальных уравнений, поскольку многие задачи механики, физики и инженерии сводятся к анализу колебательных решений как обыкновенных, так и частных уравнений. В статье применен метод характеристик, установлены достаточные условия для существования и единственности периодических по части переменныхрешения в широком смысле для линейной бесконечной системы уравнений в частных производных. Также приведеныопределения решений в широком смысле для бесконечных систем первого порядка в частных производных.

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On a Boundary Value Problem for High-Order Hyperbolic Equation With Impulse Discrete Memory

Assanova,

Bimenova,

Minglibayeva

et al. 2024

jour

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The investigation focuses on a boundary value problem for a high-order hyperbolic equation with impulse discrete memory in a rectangular domain. By introducing new functions, the problem is transformed into a set of boundary value problems for a first-order differential equation with impulse discrete memory, which depends on unknown functions and integral relations. D.S. Dzhumabaev's parametrization method is applied to this equivalent problem. The domain is divided according to the time variable, and functional parameters representing discrete memory values are introduced within the interior domains. As a result, the family of boundary value problems for the first-order differential equation with impulse discrete memory and unknown functions is converted into an equivalent family of integral-multipoint boundary value problems involving functional parameters and unknown functions. These equivalent problems include initial value problems for first-order differential equations related to the new functions. The solutions to the initial value problems are expressed using Volterra integral equations. By substituting these solutions into the boundary and impulse conditions, a system of linear functional equations concerning the functional parameters is derived. An algorithm is developed to solve the equivalent problem, and sufficient conditions for the unique solvability of the family of integral-multipoint boundary value problems with functional parameters and unknown functions are provided. Additionally, sufficient conditions for the unique solvability of the original boundary value problem for the high-order hyperbolic equation with impulse discrete memory are established based on the initial data.

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A generalized integral problem for a system of hyperbolic equations and its applications

Cited by 3 publications

References 25 publications

On a non-local problem for system of partial differential equations of hyperbolic type in a specific domain

On a non-local problem for system of partial differential equations of hyperbolic type in a specific domain

Построение Решения В Широком Смысле Линейной Счетной Системы Дифференциальных Уравнений

On a Boundary Value Problem for High-Order Hyperbolic Equation With Impulse Discrete Memory

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