Controllability of nonlinear degenerate parabolic cascade systems

Abstract

This article studies of null controllability property of nonlinear coupled one dimensional degenerate parabolic equations. These equations form a cascade system, that is, the solution of the first equation acts as a control in the second equation and the control function acts only directly on the first equation. We prove positive null controllability results when the control and a coupling set have nonempty intersection.

Keywords

• Null controllability
• nonlinear coupled systeml Carleman inequality
• observability inequality
• degenerate parabolic system
• Kakutani fixed point