Direct and inverse problem for bi-wave equation with time-dependent coefficients from partial data

In this article, we study a direct and an inverse problem for the bi-wave operator $({\mathrm{\square }}^2)$ along with second and lower order time-dependent perturbations. In the direct problem, we prove that the operator is well-posed, given initial and boundary data in suitable function spaces. In the inverse problem, we prove uniqueness of the lower order time-dependent perturbations from the partial input-output operator. The restriction in the measurements are considered by restricting some of the Neumann data over a portion of the lateral boundary.