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\begin{document}

\title{On a general degenerate/singular parabolic equation with a nonlocal
space term}



\author[1]{Brahim Allal}%
\author[2]{Genni Fragnelli}%
\author[3]{Jawad Salhi}%
\affil[1]{Universite Hassan 1er de Settat}%
\affil[2]{Università degli Studi di Bari}%
\affil[3]{Moulay Ismail University of Meknes}%


\vspace{-1em}



  
  \date{May 25, 2024}


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\begin{abstract}
In this paper we study the null controllability for the problems
associated to the operators y\_t-Ay - \textbackslash{}lambda/b(x)
y+\textbackslash{}int\_0\^{}1 K(t,x,\textbackslash{}tau)y(t,
\textbackslash{}tau) d\textbackslash{}tau, (t,x) \textbackslash{}in
(0,T)\textbackslash{}times (0,1) where Ay := ay\_\{xx\} or Ay :=
(ay\_x)\_x and the functions a and b degenerate at an interior point x0
\selectlanguage{ngerman}Ë .0; 1/. To this aim, as a first step we study the well posedness, the
Carleman estimates and the null controllability for the associated
nonhomogeneous degenerate and singular heat equations. Then,using the
Kakutani's fixed point Theorem, we deduce the null controllability
property for the initial nonlocal problems.%
\end{abstract}\selectlanguage{ngerman}%



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