Journals
Resources
About Us
Open Access

Increasing Stability of Determining Both the Potential and Source for the Biharmonic Wave Equation

Increasing Stability of Determining Both the Potential and Source for the Biharmonic Wave Equation

Year:    2025

Author:    Yuliang Wang, Yue Zhao

East Asian Journal on Applied Mathematics, Vol. 15 (2025), Iss. 2 : pp. 225–241

Abstract

This paper is concerned with the inverse scattering problems of simultaneously determining the unknown potential and unknown source for the biharmonic wave equation. We first derive an increasing stability estimate for the inverse potential scattering problem without a priori knowledge of the source function by multi-frequency active boundary measurements. The stability estimate consists of the Lipschitz type data discrepancy and the high frequency tail of the potential function, where the latter decreases as the upper bound of the frequency increases. The key ingredients in the analysis are employing scattering theory to derive an analytic domain and resolvent estimates and an application of the quantitative analytic continuation principle. Utilizing the derived stability for the inverse potential scattering, we further prove an increasing stability estimate for the inverse source problem. The main novelty of this paper is that both the source and potential functions are unknown.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.2023-205.171223

East Asian Journal on Applied Mathematics, Vol. 15 (2025), Iss. 2 : pp. 225–241

Published online:    2025-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Inverse scattering problem increasing stability biharmonic wave equation.

Author Details

Yuliang Wang

Yue Zhao

  1. Direct and inverse scattering in an optical waveguide*

    Chang, Yan

    Guo, Yukun

    Zhao, Yue

    Inverse Problems, Vol. 40 (2024), Iss. 12 P.125010

    https://doi.org/10.1088/1361-6420/ad8d76 [Citations: 1]