On a general degenerate non-autonomous parabolic equation in non-divergence form with Dirichlet or Robin boundary conditions

In this paper, we consider a non-autonomous degenerate parabolic equation in non-divergence form with Dirichlet or Robin boundary conditions. Moving beyond the restrictive case of separable coefficients, we address the general case of a diffusion coefficient a that degenerates in space and depends arbitrarily on time. We consider two types of degeneracy, weak and strong, extending the definitions from the autonomous case given in [3, 12] or [13]. We study the well-posedness of this general non-autonomous degenerate problem and establish its null-controllability via Carleman estimates devised for the associated non-homogeneous adjoint problem.