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The Heat Equaton with General Periodic Boundary Conditions



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Rodríguez Bernal, Aníbal (2017) The Heat Equaton with General Periodic Boundary Conditions. Potential Analysis, 46 (2). pp. 295-321. ISSN 09262601

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Official URL: http://link.springer.com/article/10.1007/s11118-016-9584-8


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.

Item Type:Article
Uncontrolled Keywords:Analytic semigroups; Heat equation; Periodic boundary conditions; Smoothing effect
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:40549
Deposited On:02 Feb 2017 10:02
Last Modified:12 Dec 2018 15:06

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