2005
DOI: 10.1515/156939405775199541
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Direct and inverse acoustic scattering problems involving smart obstacles

Abstract: Direct and inverse acoustic scattering problems involving smart obstacles are proposed and some ideas to study them are suggested. A smart obstacle is an obstacle that when hit by an incoming acoustic wave reacts circulating on its boundary a pressure current, that is a quantity dimensionally given by a pressure divided by a time, in order to generate a scattered wave that pursues a preassigned goal. In our models (see [6][7][8][9][10]12]) the smart obstacle pursues one of the following goals: i) to be undetec… Show more

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Cited by 4 publications
(6 citation statements)
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“…A pressure current is a quantity whose physical dimension is pressure divided by time. A mathematical model of the acoustic time-dependent and time-harmonic direct scattering problems involving smart obstacles has been suggested recently (see [4][5][6][7][8][9][10][11]) and consists in the formulation of an optimal control problem for the wave equation in the time-dependent case that reduces, in the time-harmonic case, to a constrained optimization problem with the constraints given by an exterior boundary value problem for the Helmholtz equation. The pressure current is the control variable of the optimal control problem or the independent variable of the optimization problem respectively that must be determined.…”
Section: Introductionmentioning
confidence: 99%
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“…A pressure current is a quantity whose physical dimension is pressure divided by time. A mathematical model of the acoustic time-dependent and time-harmonic direct scattering problems involving smart obstacles has been suggested recently (see [4][5][6][7][8][9][10][11]) and consists in the formulation of an optimal control problem for the wave equation in the time-dependent case that reduces, in the time-harmonic case, to a constrained optimization problem with the constraints given by an exterior boundary value problem for the Helmholtz equation. The pressure current is the control variable of the optimal control problem or the independent variable of the optimization problem respectively that must be determined.…”
Section: Introductionmentioning
confidence: 99%
“…The work presented here is only an attempt of studying these inverse problems: previous work includes [4,6] and further investigations will be presented elsewhere.…”
Section: Introductionmentioning
confidence: 99%
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