Approximate controllability of a parabolicsystem with imperfect interfaces

Issue Date

12-2015

Abstract

In this paper, the investigation of the asymptotic behavior of the approximate control for a parabolic equation with periodic rapidly oscillating coefficients depending on a parameter γ and modeling composites with interfacial resistance was completed. The approximate control and its asymptotic behavior as ε → 0 for the case −1 < γ ≤ 1was done recently in Donato & Jose (2015). The remaining case γ ≤ −1 was considered. The corrector results for the latter case given in Yang (2014) play an important role when proving this result. Following an idea introduced by Lions (1991), the approximate control is constructed as the solutions of a related transposed problem having as final data the (unique) minimum point of a suitable functional. It was then demonstrated that the control and the corresponding solution of the periodic problem converge respectively to the control and to the solution of the homogenized problem. One of the main difficulties in this study was to find the appropriate limit functionals in order to obtain the convergence results. This study addressed the problem of homogenization in the context of controllability and vice-versa, showing the interplay of two approaches in the study of partial differential equations.

Source or Periodical Title

Philippine Journal of Science

ISSN

0031-7683

Volume

144

Issue

2

Page

187-196

Document Type

Article

Physical Description

figures

Language

English

Subject

Approximate controllability, Homogenization, Interface, Jump condition, Parabolic equation, Periodic interface

Digital Copy

yes

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