CARLEMAN ESTIMATE FOR SOLUTIONS TO A DEGENERATE CONVECTION-DIFFUSION EQUATION.

This paper concerns a control system governed by a convection-diffusion equation, which is weakly degenerate at the boundary. In the governing equation, the convection is independent of the degeneracy of the equation and cannot be controlled by the diffusion. The Carleman estimate is established by means of a suitable transformation, by which the diffusion and the convection are transformed into a complex union, and complicated and detailed computations. Then the observability inequality is proved and the control system is shown to be null controllable. [ABSTRACT FROM AUTHOR]