The problem of determining the one‐dimensional matrix kernel of the system of viscoelasticity equations

Abstract

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.