Degenerate non-autonomous parabolic equation in divergence form: well-posedness and controllability via Carleman estimates

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Abstract

This paper addresses the null-controllability of a non-autonomous degenerate parabolic equation in divergence form, considering a diffusion coefficient a that degenerates in space and varies arbitrarily in time, thus generalizing the previously studied separable case in [1, 2]. Boundary conditions of Dirichlet or Robin type are imposed at the degeneracy point, while the control acts in the interior of the domain. After establishing well-posedness, we prove null-controllability by deriving new Carleman estimates for the associated non-homogeneous adjoint problem.

Keywords

null-controllability / degenerate equations / non-autonomous equations / Carleman estimates / operators in divergence form / Dirichlet and Robin boundary conditions

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