# Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

## Abstract

In three-dimensional domain a problem of identification of recourses for Benney-Luke type partial differential equation of the even order with integral form conditions, spectral parameter and small positive parameters in mixed derivatives is considered. The solution of this partial differential equation is studied in the class of regular functions. The Fourier series method is used. Using this Fourier method, is obtained a countable system of ordinary differential equations. So, the nonlocal boundary value problem is integrated as an ordinary differential equation. When we define the arbitrary integration constants there are possible five cases with respect to the spectral parameter. By the aid of given additional condition, we obtained the presentations with respect to redefinition functions. Using the Cauchy-Schwarz inequality and the Bessel inequality, we proved the absolute and uniform convergence of the obtained Fourier series.

## First Page

141

## Last Page

155

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## Recommended Citation

Rakhmonov, Farhod
(2023)
"Identification of sources in a boundary value problem for Benney-Luke type differential equation with integral conditions,"
*Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences*: Vol. 6:
Iss.
3, Article 3.

DOI: https://doi.org/10.56017/2181-1318.1254