Open AccessExact internal controllability for the wave equation in a domain with oscillating boundary with Neumann boundary condition
Author(s) -
Umberto De Maio,
Akamabadath K. Nandakumaran,
Carmen Perugia
Publication year - 2015
Publication title -
evolution equations and control theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 19
eISSN - 2163-2480
pISSN - 2163-2472
DOI - 10.3934/eect.2015.4.325
Subject(s) - controllability , neumann boundary condition , homogenization (climate) , mathematical analysis , mathematics , boundary value problem , boundary (topology) , domain (mathematical analysis) , mixed boundary condition , wave equation , homogeneous , biodiversity , ecology , combinatorics , biology
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