Null controllability of nonlinear heat equation with memory effects

We study the null controllability of a nonlinear heat type equation with nonlinearities in a bounded domain Ω ⊂ R n . The equation contains the additional integral expression including “memory function” with Dirichlet boundary conditions. The proof of the linear problem relies on Carleman-estimate and observability inequality for the adjoint equation and that the nonlinear one, on the fixed point technique.