Convexification for the inversion of a time dependent wave front in a heterogeneous medium

Klibanov，Michael V.1; Li，Jingzhi2; Zhang，Wenlong3,4

2019

10.1137/18M1236034

SIAM JOURNAL ON APPLIED MATHEMATICS   影响因子和分区

0036-1399

1095-712X

An inverse scattering problem for the 3-dimensional acoustic equation in time domain is considered. The unknown spatially distributed speed of sound is the subject of the solution of this problem. A single location of the point source is used. Using a Carleman weight function, a globally strictly convex cost functional is constructed. A new Carleman estimate is proven. Global convergence of the gradient projection method is proven. Numerical experiments are conducted.

Carleman estimate Coefficient inverse problem Convexification Global strict convexity Numerical examples

SCI ; EI

英语

通讯

Shenzhen Sci-Tech Fund[JCYJ20160530184212170] ; Shenzhen Sci-Tech Fund[JCYJ20170818153840322]

Mathematics

Mathematics, Applied

WOS:000493900600005

SIAM PUBLICATIONS

20194307567424

Wavefronts

MATHEMATICS

2-s2.0-85073618255

Scopus

1.Department of Mathematics and StatisticsUniversity of North Carolina at Charlotte,Charlotte,28223,United States
2.Department of MathematicsSouthern University of Science and Technology (SUSTech)University Town of Shenzhen,Xili, Nanshan, Shenzhen, Guangdong Province,1088 Xueyuan Boulevard,China
3.Department of MathematicsSouthern University of Science and Technology (SUSTech)University Town of Shenzhen,Xili, Nanshan, Shenzhen, Guangdong Province,1088 Xueyuan Boulevard,China
4.School of Mathematics and StatisticsWuhan University,Wuhan,430072,China

Klibanov，Michael V.,Li，Jingzhi,Zhang，Wenlong. Convexification for the inversion of a time dependent wave front in a heterogeneous medium[J]. SIAM JOURNAL ON APPLIED MATHEMATICS,2019,79(5):1722-1747.

Klibanov，Michael V.,Li，Jingzhi,&Zhang，Wenlong.(2019).Convexification for the inversion of a time dependent wave front in a heterogeneous medium.SIAM JOURNAL ON APPLIED MATHEMATICS,79(5),1722-1747.

Klibanov，Michael V.,et al."Convexification for the inversion of a time dependent wave front in a heterogeneous medium".SIAM JOURNAL ON APPLIED MATHEMATICS 79.5(2019):1722-1747.