Controllability results for the two-dimensional heat equation with mixed boundary conditions using Carleman inequalities: a linear and a semilinear case

ABSTRACT

In this paper, we prove controllability results for a two-dimensional semilinear heat equation with mixed boundary conditions. It is well-known that mixed boundary conditions can present a singular behaviour of the solution. First, we will prove global Carleman estimates then we will use these inequalities to obtain controllability results.

Keywords:

• Mixed boundary conditions
• controllability
• singularities
• Carleman inequalities
• semilinear parabolic equations

AMS Subject Classifications:

• 35K58
• 93B05

Acknowledgements

The authors would like to warmly thank Assia Benabddallah from Aix Marseille University for helpful discussions and constructive comments.

Notes

No potential conflict of interest was reported by the authors.