Furtivity and masking problems
in time dependent acoustic obstacle scattering
Dipartimento di Matematica e Fisica,
Università di Camerino, Via Madonna delle Carceri,
62032 Camerino (MC) Italy,
Istituto di Teoria delle Decisioni e Finanza Innovativa (DE.F.IN.),
Università di Ancona, Piazza Martelli 8,
60121 Ancona, Italy,
Dipartimento di Matematica ``G. Castelnuovo'', Università di
Roma ``La Sapienza'', Piazzale Aldo Moro 2,
00185 Roma, Italy
We consider ``furtivity" and ``masking" problems in
time dependent acoustic obstacle scattering. Roughly speaking a
``furtivity" (``masking") problem consists in making ``undetectable"
(``unrecognizable") an object immersed in a medium where an acoustic wave
that scatters on the object is propagating. The detection (recognition) of
the obstacle must be made through the knowledge of the acoustic field
scattered by the object when hit by the propagating wave.
These problems are interesting
in several application fields.
We formulate a mathematical model for the ``furtivity" and ``masking"
problems considered consisting in optimal control problems for the wave
equation. Using the Pontryagin maximum principle we show that the solution
of these control problems can be characterized as the solution of a
suitable exterior problem for a system of two coupled wave equations. The
numerical solution of these systems involving partial differential
equations in four (space, time) independent variables is a critical issue
when reliable and efficient procedures to solve the furtivity or masking
problem are required. High performance parallel algorithms are desirable
to solve these systems. We suggest a computational method well suited for
parallel computing and based on the operator expansion method introduced
in  and developed by the authors and some co-authors in
-. Finally we make some comments on
the possible extension of this work to electromagnetic obstacle scattering
and fluid mechanics.
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