Electron. J. Diff. Equ., Vol. 2016 (2016), No. 219, pp. 1-25.

Controllability of nonlinear degenerate parabolic cascade systems

Mamadou Birba, Oumar Traore

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.

Submitted March 21, 2016. Published August 16, 2016.
Math Subject Classifications: 35K65, 93B05, 93B07, 93C20.
Key Words: Null controllability; nonlinear coupled systeml Carleman inequality; observability inequality; degenerate parabolic system; Kakutani fixed point.

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Mamadou Birba
Laboratoire LAMI, Universitá Ouaga I
Professeur Joseph Ki Zerbo
01 BP 7021 Ouaga 01, Burkina Faso
email: birba12mamadou@gmail.com
Oumar Traore
Département de Mathématiques de la Decision
Université Ouaga 2
12 BP 417 Ouaga 12, Burkina Faso
email: traore.oumar@univ-ouaga.bf

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