WELL-POSEDNESS AND LONG-TIME BEHAVIOR FOR A CLASS OF DOUBLY NONLINEAR EQUATIONS
WELL-POSEDNESS AND LONG-TIME BEHAVIOR FOR A CLASS OF DOUBLY NONLINEAR EQUATIONS
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一类双非线性方程组的适定性和长时间行为
DOI：
10.3934/dcds.2007.18.15
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发表时间：
2006
影响因子：
1.1
通讯作者：
U. Stefanelli
中科院分区：
文献类型：
--
作者：
Giulio Schimperna;A. Segatti;U. Stefanelli
本文研究了一类双非线性抛物包含问题，
$\mathcal A（u_t）+\mathcal B（u）$\mathcal f.
存在
在适当的条件下，
单调性、非单调性和结构
对运营商的假设
$\mathcal A $和$\mathcal B$，特别是它们都被假设为
是L^2（\Omega）上泛函的次微分
由于分析中包含了无界算子$\mathcal A $，
这一理论部分地扩展了科利和维辛丁的工作[24]。
此外，在其他假设下，
在$\mathcal B$上，证明了解的唯一性.最后，
的表征
的$\omega$-极限解集，我们
研究轨迹的收敛性，
限制点。
This paper addresses a doubly nonlinear parabolic inclusion of the form
$\mathcal A (u_t)+\mathcal B (u)$ ∋ f.
Existence
of a solution is proved under suitable
monotonicity, coercivity, and structure
assumptions on the operators
$\mathcal A $ and $\mathcal B$, which in particular are both supposed
to be subdifferentials of functionals on $L^2(\Omega)$.
Since unbounded operators $\mathcal A $ are included in the analysis,
this theory partly extends Colli & Visintin's work [24].
Moreover, under additional hypotheses
on $\mathcal B$, uniqueness of the solution is proved. Finally,
a characterization
of $\omega$-limit sets of solutions is given, and we
investigate the convergence of trajectories to
limit points.