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Inverse source problems in electrodynamics

  • * Corresponding author: Yue Zhao

    * Corresponding author: Yue Zhao
The research of PL was supported in part by the NSF grant DMS-1151308. The work of GH is supported by the NSFC grant (No. 11671028) and NSAF grant (No. U1530401). The research of XL is supported by the NNSF of China under grant 11571355 and the Youth Innovation Promotion Association, CAS.
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  • This paper concerns inverse source problems for the time-dependent Maxwell equations. The electric current density is assumed to be the product of a spatial function and a temporal function. We prove uniqueness and stability in determining the spatial or temporal function from the electric field, which is measured on a sphere or at a point over a finite time interval.

    Mathematics Subject Classification: Primary: 35R30; Secondary: 35Q61.


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  • Figure 1.  (left): A Gaussian-modulated sinusoidal pulse function $\chi$ with $\omega = 6$, $\sigma = 1.6$, $\tau = 3$; (right): Fourier spectrum of $\chi$

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