Analysis of the Avalos–Triggiani problem for the linear Oskolkov system of the highest order and a system of wave equations

The Avalos–Triggiani problem for a system of wave equations and a linear Oskolkov system of the highest order is investigated. The mathematical model contains a linear Oskolkov system describing the flow of an incompressible viscoelastic Kelvin–Voigt fluid of of the highest order, and a wave vector equation corresponding to some structure immersed in the specified fluid. Based on the method proposed by the authors of this problem, the theorem of the existence of the unique solution to the Avalos–Triggiani problem for the indicated systems is proved.