INVERSE PROBLEM FOR A SECOND-ORDER HYPERBOLIC INTEGRO-DIFFERENTIAL EQUATION WITH VARIABLE COEFFICIENTS FOR LOWER DERIVATIVES

被引：2

作者：

Durdiev, D. K. ^{[1
]}

Totieva, Z. D. ^{[2
,3
]}

机构：

[1] Bukhara State Univ, Bukhara Dept, Math Inst, 11 Mukhammad Iqbol Str, Bukhara 200177, Uzbekistan

[2] Russian Acad Sci, Southern Math Inst, Vladikavkaz Sci Ctr, 93A,Markova Str, Vladikavkaz 362002, Russia

[3] North Ossetian State Univ, 46 Vatutina Str, Vladikavkaz 362025, Russia

来源：

SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA | 2020年 / 17卷

关键词：

inverse problem; hyperbolic integro-differential equation; Volterra integral equation; stability; delta function; kernel; ONE-DIMENSIONAL KERNEL;

D O I：

10.33048/semi.2020.17.084

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The problem of determining the memory of a medium from a second-order equation of hyperbolic type with a constant principal part and variable coefficients for lower derivatives is considered. The method is based on the reduction of the problem to a non-linear system of Volterra equations of the second kind and uses the fundamental solution constructed by S. L. Sobolev for hyperbolic equation with variable coefficients. The theorem of global uniqueness, stability and the local theorem of existence are proved.

引用

页码：1106 / 1127

页数：22

共 50 条

[21] Inverse/observability estimates for second-order hyperbolic equations with variable coefficients
Lasiecka, I
Triggiani, R
Yao, PF
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1999, 235 (01) : 13 - 57
[22] Uniqueness of the Kernel Determination Problem in a Integro-Differential Parabolic Equation with Variable Coefficients
Durdiev, D. K.
Nuriddinov, J. Z.
RUSSIAN MATHEMATICS, 2023, 67 (11) : 1 - 11
[23] Uniqueness of the Kernel Determination Problem in a Integro-Differential Parabolic Equation with Variable Coefficients
D. K. Durdiev
J. Z. Nuriddinov
Russian Mathematics, 2023, 67 : 1 - 11
[24] Inverse problems for second order integro-differential operators
Yurko, Vjacheslav
APPLIED MATHEMATICS LETTERS, 2017, 74 : 1 - 6
[25] The Cauchy problem for complete second-order hyperbolic differential equations with variable domains of operator coefficients
F. E. Lomovtsev
Differential Equations, 2000, 36 : 605 - 612
[26] The Cauchy problem for complete second-order hyperbolic differential equations with variable domains of operator coefficients
Lomovtsev, FE
DIFFERENTIAL EQUATIONS, 2000, 36 (04) : 605 - 612
[27] REACHABILITY OF A SECOND-ORDER INTEGRO-DIFFERENTIAL EQUATION ON RIEMANNIAN MANIFOLD FOR A VISCOELASTICITY MODEL
Zhou, Kang
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2019,
[28] On the second-order neutral Volterra integro-differential equation and its numerical solution
Amirali, Ilhame
Fedakar, Burcu
Amiraliyev, Gabil M.
APPLIED MATHEMATICS AND COMPUTATION, 2024, 476
[29] A stability estimate for the solution to the problem of determining the coefficients of the first derivatives in a second-order hyperbolic equation
Romanov, VG
DOKLADY MATHEMATICS, 2000, 62 (01) : 81 - 83
[30] Numerical methods for solving a hyperbolic inverse integro-differential problem
J Inverse Ill Posed Probl, 6 (535):

← 1 2 3 4 5 →