On an optimal control problem for the wave equation with input on an unknown surface
Vol. 16 (2009), No. 4, Page 501--524.
Ton, Bui An
On an optimal control problem for the wave equation with input on an unknown surface
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]
Abstract:
An optimal control problem for the wave equation with Dirichlet boundary conditions, initial data in \(L^{2}(\Omega)\times H^{-1}(\Omega)\) and input \(\mu\) on an unknown interior surface,is studied.Using control techniques and the generalized gradients, feedback laws for an approximating system yielding the support of the Radon measure \(\,\mu\) from observed values of the solution in a fixed subregion, are established.
Keywords: wave equation, Radon measure source, transpose solution, input on a surface, feedback laws
Mathematics Subject Classification (2000): 35L05, 49J20, 49N45
Mathematical Reviews Number: MR2650518
Received: 2007-01-30
