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

Umberto De Maio; Akamabadath K.  Nandakumaran; Carmen  Perugia

doi:10.3934/eect.2015.4.325

Article Contents

2015, Volume 4, Issue 3: 325-346. Doi: 10.3934/eect.2015.4.325

This issue Previous Article Cauchy problem for a sixth order Cahn-Hilliard type equation with inertial term Next Article A backward uniqueness result for the wave equation with absorbing boundary conditions

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

1.
Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli “Federico II”, DMA “R. Caccioppoli”, Complesso Monte S. Angelo, via Cintia, 80126 Napoli
2.
Department of Mathematics, Indian Institute of Science, Bangalore-560012

Received: November 30, 2014

Revised: March 31, 2015

Published: August 2015

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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.

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Mathematics Subject Classification: Primary: 35B27, 35B40, 93B05, 76M50; Secondary: 49J20.

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