The Heat Equaton with General Periodic Boundary Conditions

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• 作者：Aníbal Rodríguez-Bernal
• 关键词：Periodic boundary conditions ; Heat equation ; Smoothing effect ; Analytic semigroups
• 刊名：Potential Analysis
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：46
• 期：2
• 页码：295-321
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Potential Theory; Probability Theory and Stochastic Processes; Geometry; Functional Analysis;
• 出版者：Springer Netherlands
• ISSN：1572-929X
• 卷排序：46

文摘

In this paper we address the well posedness of the linear heat equation under general periodic boundary conditions in several settings depending on the properties of the initial data. We develop an Lq theory not based on separation of variables and use techniques based on uniform spaces. We also allow less directions of periodicity than the dimension of the problem. We obtain smoothing estimates on the solutions. Also, based on symmetry arguments, we handle Dirichlet or Neumann boundary conditions in some faces of the unit cell.