Uniqueness in determining a sound-hard ball with the modulus of a far-field datum

ABSTRACT

In this paper, various original properties of the Bessel and spherical Bessel functions are presented, based on which we prove a novel uniqueness result of an inverse acoustic obstacle scattering problem, that is, a sound-hard ball with a known center can be uniquely determined by the modulus of a single far-field datum corresponding to a single incident plane wave.

KEYWORDS:

• Inverse acoustic obstacle scattering
• sound-hard ball
• uniqueness
• modulus
• one incident wave

AMS SUBJECT CLASSIFICATIONS:

• 78A46
• 35J25

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the Guangdong Natural Science Foundation [grant number 2016A030313074], by a research fund from Jinan University [grant number 21617414].