An analysis of the Avalos–Triggiani problem for the linear Oskolkov system of non-zero order and a system of wave equations

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