具有波纹边界的高维薄域非线性边界条件的拟线性问题

IF 2.1 2区 数学 Q1 MATHEMATICS Advanced Nonlinear Studies Pub Date : 2023-01-01 DOI:10.1515/ans-2023-0101
J. C. Nakasato, M. Pereira
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引用次数: 0

摘要

摘要在这项工作中,我们分析了一类定义在振荡(N+1)\左(N+1。我们还允许粗糙边界上的单调非线性边界条件,其大小取决于域的压缩。根据粗糙度的强度和非线性边界条件下的一个反应系数项,我们得到了在N维开有界集上建立有效齐化极限的不同状态。为了做到这一点,我们结合了单调算子分析技术和用于处理渐近分析和均匀化问题的展开方法。
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Quasilinear problems with nonlinear boundary conditions in higher-dimensional thin domains with corrugated boundaries
Abstract In this work, we analyze the asymptotic behavior of a class of quasilinear elliptic equations defined in oscillating ( N + 1 ) \left(N+1) -dimensional thin domains (i.e., a family of bounded open sets from R N + 1 {{\mathbb{R}}}^{N+1} , with corrugated bounder, which degenerates to an open bounded set in R N {{\mathbb{R}}}^{N} ). We also allow monotone nonlinear boundary conditions on the rough border whose magnitude depends on the squeezing of the domain. According to the intensity of the roughness and a reaction coefficient term on the nonlinear boundary condition, we obtain different regimes establishing effective homogenized limits in N N -dimensional open bounded sets. In order to do that, we combine monotone operator analysis techniques and the unfolding method used to deal with asymptotic analysis and homogenization problems.
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来源期刊
CiteScore
3.00
自引率
5.60%
发文量
22
审稿时长
12 months
期刊介绍: Advanced Nonlinear Studies is aimed at publishing papers on nonlinear problems, particulalry those involving Differential Equations, Dynamical Systems, and related areas. It will also publish novel and interesting applications of these areas to problems in engineering and the sciences. Papers submitted to this journal must contain original, timely, and significant results. Articles will generally, but not always, be published in the order when the final copies were received.
期刊最新文献
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