Thin domains with non-smooth periodic oscillatory boundaries

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• 作者：José ; M. Arrieta^a ; ^b ; Manuel Villanueva-Pesqueira^a ; ^{manuelvillanueva@mat.ucm.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Thin domain ; Oscillatory boundary ; Homogenization ; Unfolding method
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：446
• 期：1
• 页码：130-164
• 全文大小：829 K

文摘

In this work we study in detail how to adapt the unfolding operator method to thin domains with periodic oscillatory boundaries. We present the unfolding method as a general approach which allows us to analyze the behavior of the solutions of a Neumann problem for equation −Δu+u=f$-\mathrm{\Delta }u+u=f$ posed in two-dimensional thin domains with an oscillatory boundary. Assuming very mild hypothesis on the regularity of the oscillatory boundary we obtain the homogenized limit problem and corrector results for the three different cases depending on the order of the period of the oscillations.