  In this paper we deal with uniqueness of solutions to the following problem
\[ \begin{cases} \begin{split} & u_t-\Delta_p u=H(t,x,\nabla u) &\quad
\text{in}\quad Q_T,\\ & u (t,x) =0 &\quad \text{on}\quad(0,T)\times \partial
\Omega,\\ & u(0,x)=u_0(x) &\quad \displaystyle\text{in }\quad \Omega
\end{split} \end{cases} \] where $Q_T=(0,T)\times \Omega$ is the parabolic
cylinder, $\Omega$ is an open subset of $\mathbb{R}^N$, $N\ge2$, $1<p<N$, and
the right hand side $\displaystyle H(t,x,\xi):(0,T)\times\Omega \times
\mathbb{R}^N\to \mathbb{R}$ exhibits a superlinear growth with respect to the
gradient term.
