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The problem of determining the one‐dimensional matrix kernel of the system of viscoelasticity equations
Author(s) -
Durdiev Durdimurod Kalandarovich,
Totieva Zhanna Dmitrievna
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5267
Subject(s) - mathematics , mathematical analysis , scalar (mathematics) , kernel (algebra) , integral equation , inverse problem , volterra integral equation , partial differential equation , matrix (chemical analysis) , independent equation , pure mathematics , geometry , materials science , composite material
The integro‐differential system of viscoelasticity equations with a source of explosive type is considered. It is assumed that the coefficients of the equations depend only on one spatial variable. The problem of determining the matrix kernel included in the integral terms of the equations is studied. The solution of the problem is reduced to a series of inverse problems for scalar hyperbolic equations. For each case, the inverse problem is replaced by an equivalent system of integral equations for unknown functions. The principle of constricted mapping in the space of continuous functions with weighted norms to the latter is applied. The theorems of global unique solvability are proved, and the stability estimates of solution to the inverse problems are obtained.