Uniqueness to Some Inverse Source Problems for the Wave Equation in Unbounded Domains  

作　　者：Guang-hui HU Yavar KIAN Yue ZHAO 

机构地区：[1]Beijing Computational Science Research Center,Beijing 100193,China [2]Aix Marseille Univ,Universit’e de Toulon,CNRS,CPT,Marseille,France [3]School of Mathematics and Statistics,Central China Normal University,Wuhan 430079,China

出　　处：《Acta Mathematicae Applicatae Sinica》2020年第1期134-150,共17页应用数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(No.11671028);the NSAF grant(No.U1930402)in the National Natural Science Foundation of China;supported by the French National Research Agency ANR(project MultiOnde)grant ANR-17-CE40-0029。

摘　　要：This paper is concerned with inverse acoustic source problems in an unbounded domain with dynamical boundary surface data of Dirichlet kind.The measurement data are taken at a surface far away from the source support.We prove uniqueness in recovering source terms of the form f(x)g(t)and f(x1,x2,t)h(x3),where g(t)and h(x3)are given and x=(x1,x2,x3)is the spatial variable in three dimensions.Without these a priori information,we prove that the boundary data of a family of solutions can be used to recover general source terms depending on both time and spatial variables.For moving point sources radiating periodic signals,the data recorded at four receivers are prove sufficient to uniquely recover the orbit function.Simultaneous determination of embedded obstacles and source terms was verified in an inhomogeneous background medium using the observation data of infinite time period.Our approach depends heavily on the Laplace transform.

关 键 词：INVERSE SOURCE problems LAPLACE transform moving point SOURCE UNIQUENESS 

分 类 号：O42[理学—声学] O175[理学—物理]