JournalspmVol. 68 / No. 3DOI 10.4171/pm/1895

Null controllability of degenerate parabolic cascade systems

  • El Mustapha Ait Ben Hassi

    Université Cadi Ayyad, Marrakech, Morocco
  • Farid Ammar Khodja

    Université de Franche-Comté, Besançon, France
  • Abdelkarim Hajjaj

    Université Hassan 1, Settat, Morocco
  • Lahcen Maniar

    Université Cadi Ayyad, Marrakech, Morocco
Null controllability of degenerate parabolic  cascade systems cover

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Abstract

In this paper, we study the null controllability of degenerate semilinear cascade parabolic systems with one control force. The key tool is the Carleman estimates developed recently for degenerate one dimension parabolic equations. We develop a Carleman estimate for these systems and then an observability inequality for the linear adjoint system. We conclude by linearization and fixed point arguments.