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.
Exact internal controllability for the wave equation in a domain with oscillating boundary with Neumann boundary condition / De Maio, U.; Nandakumaran, A. K.; Perugia, C.. - In: EVOLUTION EQUATIONS AND CONTROL THEORY. - ISSN 2163-2480. - 4:3(2015), pp. 325-346. [10.3934/eect.2015.4.325]
Exact internal controllability for the wave equation in a domain with oscillating boundary with Neumann boundary condition
U. De Maio;
2015
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
