UNIQUENESS OF THE INVERSE TRANSMISSION SCATTERING WITH A CONDUCTIVE BOUNDARY CONDITION

doi:10.1007/s10473-021-0318-7

Abstract

Abstract: This paper considers the inverse acoustic wave scattering by a bounded penetrable obstacle with a conductive boundary condition. We will show that the penetrable scatterer can be uniquely determined by its far-field pattern of the scattered field for all incident plane waves at a fixed wave number. In the first part of this paper, adequate preparations for the main uniqueness result are made. We establish the mixed reciprocity relation between the far-field pattern corresponding to point sources and the scattered field corresponding to plane waves. Then the well-posedness of a modified interior transmission problem is deeply investigated by the variational method. Finally, the a priori estimates of solutions to the general transmission problem with boundary data in $L^{p}(\partial\Omega)$ ($1

Key words: Acoustic wave, uniqueness, mixed reciprocity relation, modified interior transmission problem, a priori estimates

CLC Number:

35P25

Jianli XIANG, Guozheng YAN. UNIQUENESS OF THE INVERSE TRANSMISSION SCATTERING WITH A CONDUCTIVE BOUNDARY CONDITION[J].Acta mathematica scientia,Series B, 2021, 41(3): 925-940.

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