The inverse problem for determining the right part of the pseudo-parabolic equation

Abstract

In this pap er the inverse problem of determining a solution and an unknown right-hand side thatdep ends only on spatial variable for the linear pseudo-parab olic equation of the third order isinvestigated. In inverse problems, together with the initial and b oundary conditions also consideran additional information, the need for which is due to the presence of unknown co efficients or theright side of the equation. In this pap er, as additional information the integral overdeterminationcondition is considered. Inverse problems of determining the right-hand side of a differential equation arise in the mathematical mo deling of some physical pro cesses in the case when, in additionto solving the equation, it is necessary to restore the action of external sources. To day, studiesof direct and inverse problems for pseudo-parab olic equations are rapidly developing due to theneeds of mo deling and pro cess control in thermophysics, hydro dynamics and continuum mechanics. Similar pseudo-parab olic equations to considered in this pap er arise in the description of heatand mass transfer pro cesses, pro cesses of motion of non-Newtonian fluids, wave pro cesses, andin many other areas. Using series expansion, the existence and uniqueness theorems of classicalsolutions to this problem are proved. The result of this work is a solution presented in the seriesform, which allows the necessary numerical calculations to b e p erformed with a given accuracy.

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Published
2020-04-05
How to Cite
KHOMPYSH, Kh.; SHAKIR, A.. The inverse problem for determining the right part of the pseudo-parabolic equation. Journal of Mathematics, Mechanics and Computer Science, [S.l.], v. 105, n. 1, p. 87-98, apr. 2020. ISSN 2617-4871. Available at: <https://bm.kaznu.kz/index.php/kaznu/article/view/684>. Date accessed: 07 june 2020.
Keywords Inverse problem, pseudoparabolic equations, theorems of the existence and uniqueness of the solution, classical solution