Ricerc@Sapienza

In this paper we deal with uniqueness of solutions to the following problem
\[ \begincases \beginsplit & u_t-\Delta_p u=H(t,x,\nabla u) &\quad
\textin\quad Q_T,\\ & u (t,x) =0 &\quad \texton\quad(0,T)\times \partial
\Omega,\\ & u(0,x)=u_0(x) &\quad \displaystyle\textin \quad \Omega
\endsplit \endcases \] where $Q_T=(0,T)\times \Omega$ is the parabolic
cylinder, $\Omega$ is an open subset of $\mathbbR^N$, $N\ge2$, $1

the right hand side $\displaystyle H(t,x,\xi):(0,T)\times\Omega \times
\mathbbR^N\to \mathbbR$ exhibits a superlinear growth with respect to the
gradient term.