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.
Large time behavior for solutions of nonlinear parabolic problems with sign-changing measure data / Petitta, Francesco. - In: ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 1072-6691. - 132:(2008), pp. 1-10.
Large time behavior for solutions of nonlinear parabolic problems with sign-changing measure data.
PETITTA, FRANCESCO
2008
Abstract
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.File | Dimensione | Formato | |
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