An inverse problem for a third order PDE arising in high-intensity ultrasound: Global uniqueness and stability by one boundary measurement

Shitao Liu; Roberto Triggiani

doi:10.1515/jip-2012-0096

Published by De Gruyter November 2, 2013

An inverse problem for a third order PDE arising in high-intensity ultrasound: Global uniqueness and stability by one boundary measurement

Shitao Liu and Roberto Triggiani

From the journal Journal of Inverse and Ill-Posed Problems

https://doi.org/10.1515/jip-2012-0096

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Abstract.

In this paper, we consider an inverse problem for the linearized Jordan–Moore–Gibson–Thompson equation, which is a third-order (in time) PDE that arises in nonlinear acoustic waves modeling high-intensity ultrasound. Both canonical recovery problems are investigated: (i) uniqueness and (ii) stability, by use of just one boundary measurement. Our approach relies on the dynamical decomposition of the Jordan–Moore–Gibson–Thompson equation given in [Math. Methods Appl. Sci. 35 (2012), 1896–1929].

Keywords: Inverse problem; third-order PDE equation; uniqueness; stability

Received: 2012-12-09

Published Online: 2013-11-02

Published in Print: 2013-12-01

An inverse problem for a third order PDE arising in high-intensity ultrasound: Global uniqueness and stability by one boundary measurement

Abstract.

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