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Controllability for degenerate/singular parabolic systems involving memory terms

  • * Corresponding author: Genni Fragnelli

    * Corresponding author: Genni Fragnelli 

To the memory of Rosa Maria Mininni

$ ^* $ G.F. is a member of the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM) and a member of UMI "Modellistica Socio-Epidemiologica (MSE)". She is supported by the FFABR Fondo per il finanziamento delle attività base di ricerca 2017, by the INdAM - GNAMPA Project 2020 Problemi inversi e di controllo per equazioni di evoluzione e loro applicazioni.
** J.S. thanks the University of Bari Aldo Moro, where he was Visiting Professor when this work was written

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  • In this paper we deal with the null controllability for degenerate/singular parabolic systems with memory terms. To this aim, we first prove the null controllability property for some auxiliary nonhomogeneous degenerate/singular problems via new Carleman estimates for their corresponding adjoint systems. Then, under a condition on the kernels, using the Kakutani's fixed point theorem, we deduce null controllability results for the initial problems with memory.

    Mathematics Subject Classification: Primary: 93B05, 93B07, 35K65; Secondary: 93C20.


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