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Evolution Equations and Control Theory (EECT)
 

Exact internal controllability for the wave equation in a domain with oscillating boundary with Neumann boundary condition

Pages: 325 - 346, Volume 4, Issue 3, September 2015      doi:10.3934/eect.2015.4.325

 
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Umberto De Maio - Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli “Federico II”, DMA “R. Caccioppoli”, Complesso Monte S. Angelo, via Cintia, 80126 Napoli, Italy (email)
Akamabadath K. Nandakumaran - Department of Mathematics, Indian Institute of Science, Bangalore-560012, India (email)
Carmen Perugia - Department of Mathematics, Indian Institute of Science, Bangalore-560012, India (email)

Abstract: In this paper, we study the exact controllability of a second order linear evolution equation in a domain with highly oscillating boundary with homogeneous Neumann boundary condition on the oscillating part of boundary. Our aim is to obtain the exact controllability for the homogenized equation. The limit problem with Neumann condition on the oscillating boundary is different and hence we need to study the exact controllability of this new type of problem. In the process of homogenization, we also study the asymptotic analysis of evolution equation in two setups, namely solution by standard weak formulation and solution by transposition method.

Keywords:  Wave equation, homogenization, oscillating boundary, exact controllability.
Mathematics Subject Classification:  Primary: 35B27, 35B40, 93B05, 76M50; Secondary: 49J20.

Received: December 2014;      Revised: April 2015;      Available Online: September 2015.

 References