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We are concerned with the inverse problem of identifying magnetic anomalies with varing parameters beneath the Earth using geomagnetic monitoring. Observations of the change in Earths magnetic field--the secular variation--provide information about the anomalies as well as their variations. In this paper, we rigorously establish the unique recovery results for this magnetic anomaly detection problem. We show that one can uniquely recover the locations, the variation parameters including the growth or decaying rates as well as their material parameters of the anomalies. This paper extends the existing results in [8] by two of the authors to varying anomalies.
Divergence-free symmetric tensors seem ubiquitous in Mathematical Physics. We show that this structure occurs in models that are described by the so-called second variational principle, where the argument of the Lagrangian is a closed differential fo
We study functional and spectral properties of perturbations of the magnetic Laplace operator on the circle. This operator appears when considering the restriction to the unit circle of a two-dimensional Schr{o}dinger operator with the Bohm-Aharonov
This paper presents some results concerning the size of magnetic fields that support zero modes for the three dimensional Dirac equation and related problems for spinor equations. It is a well known fact that for the Schrodinger in three dimensions t
The aim of this paper is to study, in dimensions 2 and 3, the pure-power non-linear Schrodinger equation with an external uniform magnetic field included. In particular, we derive a general criteria on the initial data and the power of the non-linear
In this work we study Dirac operators on two-dimensional domains coupled to a magnetic field perpendicular to the plane. We focus on the infinite-mass boundary condition (also called MIT bag condition). In the case of bounded domains, we establish th