Kernel Determination Inverse Problem in the Moore–Gibson–Thompson Equation

We investigate an inverse problem of determining the kernel function g(t) in the third-order Moore–Gibson–Thompson (MGT) equation. First, the solution to the direct initial–boundary value problem for a homogeneous MGT equation is constructed using the Fourier spectral method. Then, based on this solution and the overdetermination condition, a Volterra-type integral equation is derived to study the inverse problem. We prove global existence and uniqueness results for the solutions of the considered problems. In addition, stability estimates for the solution of the direct and inverse problem are obtained.

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