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2007 Asymptotic behavior of solutions for parabolic operators of Leray-Lions type and measure data
Francesco Petitta
Adv. Differential Equations 12(8): 867-891 (2007).

Abstract

Let $\Omega\subseteq {\mathbb{R}^{N}}$ be a bounded open set, $N\geq 2$, and let $p>1$; we study the asymptotic behavior with respect to the time variable $t$ of the entropy solution of nonlinear parabolic problems whose model is $$ \begin{cases} u_{t}(x,t)-\Delta_{p} u(x,t)=\mu & \text{in}\ \Omega\times(0,T),\\ u(x,0)=u_{0}(x) & \text{in}\ \Omega, \end{cases} $$ where $T>0$ is any positive constant, $u_0 \in L^{1}(\Omega)$ a nonnegative function, and $\mu\in \mathcal{M}_{0}(Q)$ is a nonnegative measure with bounded variation over $Q=\Omega\times(0,T)$ 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.

Citation

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Francesco Petitta. "Asymptotic behavior of solutions for parabolic operators of Leray-Lions type and measure data." Adv. Differential Equations 12 (8) 867 - 891, 2007.

Information

Published: 2007
First available in Project Euclid: 29 April 2013

zbMATH: 1152.35323
MathSciNet: MR2340256

Subjects:
Primary: 35K55
Secondary: 35B40, 35R05

Rights: Copyright © 2007 Khayyam Publishing, Inc.

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Vol.12 • No. 8 • 2007
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