Determining the time-dependent matrix potential in a wave equation from partial boundary data

Mishra, Rohit Kumar; Vashisth, Manmohan

doi:10.1080/00036811.2020.1721476

Cited by 3 publications

(2 citation statements)

References 33 publications

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“…We refer to [10,21,22,24,26,23,27,30,33,34,50] for more works in inverse problems related to parabolic PDEs. Also, there have been a considerable amount of work done in the context of hyperbolic and dynamical Schrödinger equations (see [1,3,7,11,14,15,29,41,42,43,44,13,52,54,8,9,31,39,37,38,40,46,55,48,36] and references therein).…”

Section: Soumen Senapati and Manmohan Vashisthmentioning

confidence: 99%

Stability estimate for a partial data inverse problem for the convection-diffusion equation

Senapati

Vashisth

2022

EECT

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<p style='text-indent:20px;'>In this article, we study the stability in the inverse problem of determining the time-dependent convection term and density coefficient appearing in the convection-diffusion equation, from partial boundary measurements. For dimension <inline-formula><tex-math id="M1">\begin{document}$ n\ge 2 $\end{document}</tex-math></inline-formula>, we show the convection term (modulo the gauge term) admits log-log stability, whereas log-log-log stability estimate is obtained for the density coefficient.</p>

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Section: Soumen Senapati and Manmohan Vashisthmentioning

confidence: 99%

Stability estimate for a partial data inverse problem for the convection-diffusion equation

Senapati

Vashisth

2022

EECT

Self Cite

View full text Add to dashboard Cite

show abstract

“…We refer to [9,20,21,23,25,22,26,29,32,33,48] for more works in inverse problems related to parabolic PDEs. Also, there have been a considerable amount of work done in the context of hyperbolic and dynamical Schrödinger equations (see [1,3,6,10,13,14,28,40,41,42,43,12,50,51,7,8,30,38,36,37,39,45,52,47,35] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Stability estimate for a partial data inverse problem for the convection-diffusion equation

Senapati,

Vashisth

2021

Preprint

Self Cite

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In this article, we study the stability in the inverse problem of determining the timedependent convection term and density coefficient appearing in the convection-diffusion equation, from partial boundary measurements. For dimension n ≥ 2, we show the convection term (modulo the gauge term) admits log-log stability, whereas log-log-log stability estimate is obtained for the density coefficient.

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Partial Data Inverse Problem for Hyperbolic Equation with Time-Dependent Damping Coefficient and Potential

Liu,

Saksala,

Yan

2024

SIAM J. Math. Anal.

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Determining the time-dependent matrix potential in a wave equation from partial boundary data

Cited by 3 publications

References 33 publications

Stability estimate for a partial data inverse problem for the convection-diffusion equation

Stability estimate for a partial data inverse problem for the convection-diffusion equation

Stability estimate for a partial data inverse problem for the convection-diffusion equation

Partial Data Inverse Problem for Hyperbolic Equation with Time-Dependent Damping Coefficient and Potential

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