TY - JOUR

T1 - Inverse problems of parameter recovery in differential equations with multiple characteristics

AU - Kozhanov, A. I.

AU - Abylkayrov, U. U.

AU - Ashurova, G. R.

N1 - The work was partially supported by the grant (No. АР05132041) of the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan.

PY - 2022/3/31

Y1 - 2022/3/31

N2 - Inverse problems - the problem of finding the causes of known or given consequences. They arise when the characteristics of an object of interest to us are not available for direct observation. These are, for example, the restoration of the characteristics of the field sources according to their given values at some points, the restoration or interpretation of the original signal from the known output signal, etc. This paper studies the solvability of finding the solution of a differential equation of inverse problems. The work is devoted to the study of the solvability in Sobolev spaces of nonlinear inverse coefficient problems for differential equations of the third order with multiple characteristics. In this paper, alongside with finding the solution of one or another differential equation, it is also required to find one or more coefficients of the equation itself for us to name them inverse coefficient problems. A distinctive feature of the problems studied in this paper is that the unknown coefficient is a numerical parameter, and not a function of certain independent variables.

AB - Inverse problems - the problem of finding the causes of known or given consequences. They arise when the characteristics of an object of interest to us are not available for direct observation. These are, for example, the restoration of the characteristics of the field sources according to their given values at some points, the restoration or interpretation of the original signal from the known output signal, etc. This paper studies the solvability of finding the solution of a differential equation of inverse problems. The work is devoted to the study of the solvability in Sobolev spaces of nonlinear inverse coefficient problems for differential equations of the third order with multiple characteristics. In this paper, alongside with finding the solution of one or another differential equation, it is also required to find one or more coefficients of the equation itself for us to name them inverse coefficient problems. A distinctive feature of the problems studied in this paper is that the unknown coefficient is a numerical parameter, and not a function of certain independent variables.

KW - Inverse problems

KW - multiple characteristics

KW - numerical parameter

KW - solvability

KW - third-order equations

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85180199340&origin=inward&txGid=8c6ec1012f5007fb19fdf33752c1bad1

UR - https://www.mendeley.com/catalogue/f4ebe8b4-6af8-39f1-b3d7-3b1f316b6e83/

U2 - 10.26577/JMMCS.2022.v113.i1.01

DO - 10.26577/JMMCS.2022.v113.i1.01

M3 - Article

VL - 113

SP - 3

EP - 16

JO - KazNU Bulletin. Mathematics, Mechanics, Computer Science Series

JF - KazNU Bulletin. Mathematics, Mechanics, Computer Science Series

SN - 2617-4871

IS - 1

ER -