We recover locally in time two (smooth) unknown convolution kernels, depending on time only, in a phase-field system coupling two hyperbolic integro-differential equations, where the differential operators (of order two and four in space, respectively) appear only under the integral sign. Moreover, we can prove a global uniqueness result concerning the unknown kernels.
This journal presents original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published.