Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 132, pp. 1-10.

Title: Large time behavior for solutions of nonlinear parabolic problems
       with sign-changing measure data
  
Author: Francesco Petitta (Univ. of Oslo, Norway)

Abstract:
 Let $\Omega\subseteq \mathbb{R}^N$ 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
 $$\displaylines{
  u_{t}(x,t)-\Delta_{p} u(x,t)=\mu \quad \hbox{in } \Omega\times(0,\infty),\cr
  u(x,0)=u_{0}(x) \quad \hbox{in } \Omega,
 }$$
 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.
 
Submitted June 13, 2008. Published September 23, 2008.
Math Subject Classifications: 35B40, 35K55.
Key Words: Asymptotic behavior; nonlinear parabolic equations;
           measure data.