Large time behavior for solutions of nonlinear parabolic problems with sign-changing measure data.

et $\Omega\subseteq \mathbb{R}^N$ a bounded open set, $N\geq 2$, and let $p>1$; in this paper we study the asymptotic behavior with respect to the time variable $t$ of the entropy solution of nonlinear parabolic problems whose model is \begin{gather*} u_{t}(x,t)-\Delta_{p} u(x,t)=\mu \quad \text{in } \Omega\times(0,\infty),\\ u(x,0)=u_{0}(x) \quad \text{in } \Omega, \end{gather*} where $u_0 \in L^{1}(\Omega)$, and $\mu\in \mathcal{M}_{0}(Q)$ is a measure with bounded variation over $Q=\Omega\times(0,\infty)$ which does not charge the sets of zero $p$-capacity; moreover we consider $\mu$ that does not depend on time. In particular, we prove that solutions of such problems converge to stationary solutions.