Abstract
In this paper we study the null controllability for the problems
associated to the operators y_t-Ay - \lambda/b(x)
y+\int_0^1 K(t,x,\tau)y(t,
\tau) d\tau, (t,x) \in
(0,T)\times (0,1) where Ay := ay_{xx} or Ay :=
(ay_x)_x and the functions a and b degenerate at an interior point x0
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.