Null controllability for linear parabolic cascade systems with interior degeneracy

Abstract

We study the null controllability problem for linear degenerate parabolic systems with one control force through Carleman estimates for the associated adjoint problem. The novelty of this article is that for the first time it is considered a problem with an interior degeneracy and a control set that only requires to contain an interval lying on one side of the degeneracy points. The obtained result improves and complements a number of earlier works. As a consequence, observability inequalities are established.

Keywords

• Degenerate parabolic systems
• interior degeneracy
• one control force
• Carleman estimates, observability inequalities
• null controllability