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 · Evolution equations and control theory · 2015
In this paper, we study the exact controllability of a secondorder linear evolution equation in a domain with highlyoscillating boundary with homogeneous Neumann boundary conditionon the oscillating part of boundary. Our aim is to obtain theexact controllability for the homogenized equation. The limitproblem with Neumann condition on the oscillating boundary isdifferent and hence we need to study the exact controllability ofthis new type of problem. In the process of homogenization, wealso study the asymptotic analysis of evolution equation in twosetups, namely solution by standard weak formulation and solutionby transposition method.