Determination of a kernel and source term in an integro-differential wave equation

In the paper, an inverse problem of identifying the kernel and the source term in an integro-differential wave equation is investigated. The problem of determining the two coefficients governing the wave process is reduced to a nonlinear Volterra integral equation of the second kind with a convolution-type kernel. By introducing additional integral conditions, the problem is further transformed into a system of Volterra integral equations of the second kind. The contraction mapping principle is employed to establish the global existence and uniqueness of a solution in a space of continuous functions equipped with weighted norms.

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