In this paper, by using the Hilbert Uniqueness Method (HUM), we study the exact controllability problem described by the wave equation in a three-dimensional horizontal domain bounded at the bottom by a smooth wall and at the top by a rough wall. The latter is assumed to consist in a plane wall covered with periodically distributed asperities whose size depends on a small parameter ε > 0, and with a fixed height. Our aim is to obtain the exact controllability for the homogenized equation. In the process, we study the asymptotic analysis of wave equation in two setups, namely solution by standard weak formulation and solution by transposition method.
Exact Internal Controllability for a Hyperbolic Problem in a Domain with Highly Oscillating Boundary / DE MAIO, Umberto; A. K., Nandakumaran. - In: ASYMPTOTIC ANALYSIS. - ISSN 0921-7134. - 83:3(2013), pp. 189-206. [10.3233/ASY-2012-1153]
Exact Internal Controllability for a Hyperbolic Problem in a Domain with Highly Oscillating Boundary
DE MAIO, UMBERTO;
2013
Abstract
In this paper, by using the Hilbert Uniqueness Method (HUM), we study the exact controllability problem described by the wave equation in a three-dimensional horizontal domain bounded at the bottom by a smooth wall and at the top by a rough wall. The latter is assumed to consist in a plane wall covered with periodically distributed asperities whose size depends on a small parameter ε > 0, and with a fixed height. Our aim is to obtain the exact controllability for the homogenized equation. In the process, we study the asymptotic analysis of wave 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.
